Relevant bibliographies by topics / Dirichlet boundary condition

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  2. Dissertations / Theses
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Academic literature on the topic 'Dirichlet boundary condition'

Author: Grafiati
Published: 6 September 2023

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Journal articles on the topic "Dirichlet boundary condition"

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Cao, Shunhua, and Stewart Greenhalgh. "Attenuating boundary conditions for numerical modeling of acoustic wave propagation." GEOPHYSICS 63, no. 1 (January 1998): 231–43. http://dx.doi.org/10.1190/1.1444317.

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Four types of boundary conditions: Dirichlet, Neumann, transmitting, and modified transmitting, are derived by combining the damped wave equation with corresponding boundary conditions. The Dirichlet attenuating boundary condition is the easiest to implement. For an appropriate choice of attenuation parameter, it can achieve a boundary reflection coefficient of a few percent in a one‐wavelength wide zone. The Neumann‐attenuating boundary condition has characteristics similar to the Dirichlet attenuating boundary condition, but it is numerically more difficult to implement. Both the transmitting boundary condition and the modified transmitting boundary condition need an absorbing boundary condition at the termination of the attenuating region. The modified transmitting boundary condition is the most effective in the suppression of boundary reflections. For multidimensional modeling, there is no perfect absorbing boundary condition, and an approximate absorbing boundary condition is used.
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Park, I. Y. "Quantum “violation” of Dirichlet boundary condition." Physics Letters B 765 (February 2017): 260–64. http://dx.doi.org/10.1016/j.physletb.2016.12.026.

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Diyab, Farah, and B. Surender Reddy. "Comparison of Laplace Beltrami Operator Eigenvalues on Riemannian Manifolds." European Journal of Mathematics and Statistics 3, no. 5 (October 23, 2022): 55–60. http://dx.doi.org/10.24018/ejmath.2022.3.5.143.

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Let $\Delta_{g}$ be the Laplace Beltrami operator on a manifold $M$ with Dirichlet (resp.,Neumann) boundary conditions. We compare the spectrum of on a Riemannian manifold for Neumann boundary condition and Dirichlet boundary condition . Then we construct aneffective method of obtaining small eigenvalues for Neumann's problem.
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Turmetov, B. Kh, and V. V. Karachik. "NEUMANN BOUNDARY CONDITION FOR A NONLOCAL BIHARMONIC EQUATION." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 14, no. 2 (2022): 51–58. http://dx.doi.org/10.14529/mmph220205.

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The solvability conditions for a class of boundary value problems for a nonlocal biharmonic equation in the unit ball with the Neumann conditions on the boundary are studied. The nonlocality of the equation is generated by some orthogonal matrix. The presence and uniqueness of a solution to the proposed Neumann boundary condition is examined, and an integral representation of the solution to the Dirichlet problem in terms of the Green's function for the biharmonic equation in the unit ball is obtained. First, some auxiliary statements are established: the Green's function of the Dirichlet problem for the biharmonic equation in the unit ball is given, the representation of the solution to the Dirichlet problem in terms of this Green's function is written, and the values of the integrals of the functions perturbed by the orthogonal matrix are found. Then a theorem for the solution to the auxiliary Dirichlet problem for a nonlocal biharmonic equation in the unit ball is proved. The solution to this problem is written using the Green's function of the Dirichlet problem for the regular biharmonic equation. An example of solving a simple problem for a nonlocal biharmonic equation is given. Next, we formulate a theorem on necessary and sufficient conditions for the solvability of the Neumann boundary condition for a nonlocal biharmonic equation. The main theorem is proved based on two lemmas, with the help of which it is possible to transform the solvability conditions of the Neumann boundary condition to a simpler form. The solution to the Neumann boundary condition is presented through the solution to the auxiliary Dirichlet problem.
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Corrêa, Francisco Julio S. A., and Joelma Morbach. "A Dirichlet problem under integral boundary condition." Journal of Mathematical Analysis and Applications 478, no. 1 (October 2019): 1–13. http://dx.doi.org/10.1016/j.jmaa.2019.04.030.

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Amrouche, Cherif, and Šárka Nečasová. "Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition." Mathematica Bohemica 126, no. 2 (2001): 265–74. http://dx.doi.org/10.21136/mb.2001.134013.

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Yosaf, Asma, Shafiq Ur Rehman, Fayyaz Ahmad, Malik Zaka Ullah, and Ali Saleh Alshomrani. "Eighth-Order Compact Finite Difference Scheme for 1D Heat Conduction Equation." Advances in Numerical Analysis 2016 (May 16, 2016): 1–12. http://dx.doi.org/10.1155/2016/8376061.

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The purpose of this paper is to develop a high-order compact finite difference method for solving one-dimensional (1D) heat conduction equation with Dirichlet and Neumann boundary conditions, respectively. A parameter is used for the direct implementation of Dirichlet and Neumann boundary conditions. The introduced parameter adjusts the position of the neighboring nodes very next to the boundary. In the case of Dirichlet boundary condition, we developed eighth-order compact finite difference method for the entire domain and fourth-order accurate proposal is presented for the Neumann boundary conditions. In the case of Dirichlet boundary conditions, the introduced parameter behaves like a free parameter and could take any value from its defined domain but for the Neumann boundary condition we obtained a particular value of the parameter. In both proposed compact finite difference methods, the order of accuracy is the same for all nodes. The time discretization is performed by using Crank-Nicholson finite difference method. The unconditional convergence of the proposed methods is presented. Finally, a set of 1D heat conduction equations is solved to show the validity and accuracy of our proposed methods.
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Hayasida, Kazuya, and Masao Nakatani. "On the Dirichlet problem of prescribed mean curvature equations without H-convexity condition." Nagoya Mathematical Journal 157 (2000): 177–209. http://dx.doi.org/10.1017/s0027763000007248.

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The Dirichlet problem of prescribed mean curvature equations is well posed, if the boundery is H-convex. In this article we eliminate the H-convexity condition from a portion Γ of the boundary and prove the existence theorem, where the boundary condition is satisfied on Γ in the weak sense.
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Algazin, O. D., and A. V. Kopaev. "A Mixed Boundary Value Problem for the Laplace Equation in a semi-infinite Layer." Mathematics and Mathematical Modeling, no. 5 (February 6, 2021): 1–12. http://dx.doi.org/10.24108/mathm.0520.0000229.

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The paper offers a solution of the mixed Dirichlet-Neumann and Dirichlet-Neumann-Robin boundary value problems for the Laplace equation in the semi-infinite layer, using the previously obtained solution of the mixed Dirichlet-Neumann boundary value problem for a layer.The functions on the right-hand sides of the boundary conditions are considered to be functions of slow growth, in particular, polynomials. The solution to boundary value problems is also sought in the class of functions of slow growth. Continuing the functions on the right-hand sides of the boundary conditions on the upper and lower sides of the semi-infinite layer from the semi-hyperplane to the entire hyperplane, we obtain the Dirichlet-Neumann problem for the layer, the solution of which is known and written in the form of a convolution. If the right-hand sides of the boundary conditions are polynomials, then the solution is also a polynomial. To the solution obtained it is necessary to add the solution of the problem for a semi-infinite layer with homogeneous boundary conditions on the upper and lower sides and with an inhomogeneous boundary condition of Dirichlet, Neumann or Robin on the lateral side. This solution is written as a series. If we take a finite segment of the series, then we obtain a solution that exactly satisfies the Laplace equation and the boundary conditions on the upper and lower sides of the semi-infinite layer and approximately satisfies the boundary condition on the lateral side.An example of solving the Dirichlet-Neumann and Dirichlet-Neumann-Robin problems is considered, describing the temperature field of a semi-infinite plate the upper side of which is heat-isolated, on the lower side the temperature is set in the form of a polynomial, and the lateral side is either heat-isolated, or holds a zero temperature, or has heat exchange with a zero-temperature environment. For the first two Dirichlet-Neumann problems, the solution is obtained in the form of polynomials. For the third Dirichlet-Neumann-Robin problem, the solution is obtained as a sum of a polynomial and a series. If in this solution the series is replaced by a finite segment, then an approximate solution of the problem will be obtained, which approximately satisfies the Robin condition on the lateral side of the semi-infinite layer.
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YAKUBOV, YAKOV. "COMPLETENESS OF ROOT FUNCTIONS AND ELEMENTARY SOLUTIONS OF THE THERMOELASTICITY SYSTEM." Mathematical Models and Methods in Applied Sciences 05, no. 05 (August 1995): 587–98. http://dx.doi.org/10.1142/s0218202595000346.

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In this paper we prove the completeness of the root functions (eigenfunctions and associated functions) of an elliptic system (in the sense of Douglis-Nirenberg) corresponding to the thermoelasticity system with the Dirichlet boundary value condition. The problem is considered in a domain with a non-smooth boundary. Then an initial boundary value problem corresponding to the thermoelasticity system with the Dirichlet boundary value condition is considered. We find sufficient conditions that guarantee an approximation of a solution to the initial boundary value problem by linear combinations of some “elementary solutions” to the thermoelasticity system.
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Dissertations / Theses on the topic "Dirichlet boundary condition"

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Yang, Xue. "Neumann problems for second order elliptic operators with singular coefficients." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/neumann-problems-for-second-order-elliptic-operators-with-singular-coefficients(2e65b780-df58-4429-89df-6d87777843c8).html.

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In this thesis, we prove the existence and uniqueness of the solution to a Neumann boundary problem for an elliptic differential operator with singular coefficients, and reveal the relationship between the solution to the partial differential equation (PDE in abbreviation) and the solution to a kind of backward stochastic differential equations (BSDE in abbreviation).This study is motivated by the research on the Dirichlet problem for an elliptic operator (\cite{Z}). But it turns out that different methods are needed to deal with the reflecting diffusion on a bounded domain. For example, the integral with respect to the boundary local time, which is a nondecreasing process associated with the reflecting diffusion, needs to be estimated. This leads us to a detailed study of the reflecting diffusion. As a result, two-sided estimates on the heat kernels are established. We introduce a new type of backward differential equations with infinity horizon and prove the existence and uniqueness of both L2 and L1 solutions of the BSDEs. In this thesis, we use the BSDE to solve the semilinear Neumann boundary problem. However, this research on the BSDEs has its independent interest. Under certain conditions on both the "singular" coefficient of the elliptic operator and the "semilinear coefficient" in the deterministic differential equation, we find an explicit probabilistic solution to the Neumann problem, which supplies a L2 solution of a BSDE with infinite horizon. We also show that, less restrictive conditions on the coefficients are needed if the solution to the Neumann boundary problem only provides a L1 solution to the BSDE.
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Cheaytou, Rima. "Etude des méthodes de pénalité-projection vectorielle pour les équations de Navier-Stokes avec conditions aux limites ouvertes." Thesis, Aix-Marseille, 2014. http://www.theses.fr/2014AIXM4715.

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L'objectif de cette thèse consiste à étudier la méthode de pénalité-projection vectorielle notée VPP (Vector Penalty-Projection method), qui est une méthode à pas fractionnaire pour la résolution des équations de Navier-Stokes incompressible avec conditions aux limites ouvertes. Nous présentons une revue bibliographique des méthodes de projection traitant le couplage de vitesse et de pression. Nous nous intéressons dans un premier temps aux conditions de Dirichlet sur toute la frontière. Les tests numériques montrent une convergence d'ordre deux en temps pour la vitesse et la pression et prouvent que la méthode est rapide et peu coûteuse en terme de nombre d'itérations par pas de temps. En outre, nous établissons des estimations d'erreurs de la vitesse et de la pression et les essais numériques révèlent une parfaite concordance avec les résultats théoriques. En revanche, la contrainte d'incompressibilité n'est pas exactement nulle et converge avec un ordre de O(varepsilondelta t) où varepsilon est un paramètre de pénalité choisi assez petit et delta t le pas temps. Dans un second temps, la thèse traite les conditions aux limites ouvertes naturelles. Trois types de conditions de sortie sont étudiés et testés numériquement pour l'étape de projection. Nous effectuons des comparaisons quantitatives des résultats avec d'autres méthodes de projection. Les essais numériques sont en concordance avec les estimations théoriques également établies. Le dernier chapitre est consacré à l'étude numérique du schéma VPP en présence d'une condition aux limites ouvertes non-linéaire sur une frontière artificielle modélisant une charge singulière pour le problème de Navier-Stokes
Motivated by solving the incompressible Navier-Stokes equations with open boundary conditions, this thesis studies the Vector Penalty-Projection method denoted VPP, which is a splitting method in time. We first present a literature review of the projection methods addressing the issue of the velocity-pressure coupling in the incompressible Navier-Stokes system. First, we focus on the case of Dirichlet conditions on the entire boundary. The numerical tests show a second-order convergence in time for both the velocity and the pressure. They also show that the VPP method is fast and cheap in terms of number of iterations at each time step. In addition, we established for the Stokes problem optimal error estimates for the velocity and pressure and the numerical experiments are in perfect agreement with the theoretical results. However, the incompressibility constraint is not exactly equal to zero and it scales as O(varepsilondelta t) where $varepsilon$ is a penalty parameter chosen small enough and delta t is the time step. Moreover, we deal with the natural outflow boundary condition. Three types of outflow boundary conditions are presented and numerically tested for the projection step. We perform quantitative comparisons of the results with those obtained by other methods in the literature. Besides, a theoretical study of the VPP method with outflow boundary conditions is stated and the numerical tests prove to be in good agreement with the theoretical results. In the last chapter, we focus on the numerical study of the VPP scheme with a nonlinear open artificial boundary condition modelling a singular load for the unsteady incompressible Navier-Stokes problem
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Choulli, Mourad. "Identifiabilite d'un parametre dans une equation parabolique non lineaire monodimensionnelle." Toulouse 3, 1987. http://www.theses.fr/1987TOU30245.

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Etude, essentiellement basee sur des techniques utilisant le principe du maximum pour les equations paraboliques lineaires, permettant de discuter du probleme d'identifiabilite du parametre qui apparait dans une equation de diffusion non lineaire
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Matsui, Kazunori. "Asymptotic analysis of an ε-Stokes problem with Dirichlet boundary conditions." Thesis, Karlstads universitet, Institutionen för matematik och datavetenskap (from 2013), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-71938.

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In this thesis, we propose an ε-Stokes problem connecting the Stokes problem and the corresponding pressure-Poisson equation using one pa- rameter ε > 0. We prove that the solution to the ε-Stokes problem, converges as ε tends to 0 or ∞ to the Stokes and pressure-Poisson prob- lem, respectively. Most of these results are new. The precise statements of the new results are given in Proposition 3.5, Theorem 4.1, Theorem 5.2, and Theorem 5.3. Numerical results illustrating our mathematical results are also presented.
STINT (DD2017-6936) "Mathematics Bachelor Program for Efficient Computations"
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Couture, Chad. "Steady States and Stability of the Bistable Reaction-Diffusion Equation on Bounded Intervals." Thesis, Université d'Ottawa / University of Ottawa, 2018. http://hdl.handle.net/10393/37110.

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Reaction-diffusion equations have been used to study various phenomena across different fields. These equations can be posed on the whole real line, or on a subinterval, depending on the situation being studied. For finite intervals, we also impose diverse boundary conditions on the system. In the present thesis, we solely focus on the bistable reaction-diffusion equation while working on a bounded interval of the form $[0,L]$ ($L>0$). Furthermore, we consider both mixed and no-flux boundary conditions, where we extend the former to Dirichlet boundary conditions once our analysis of that system is complete. We first use phase-plane analysis to set up our initial investigation of both systems. This gives us an integral describing the transit time of orbits within the phase-plane. This allows us to determine the bifurcation diagram of both systems. We then transform the integral to ease numerical calculations. Finally, we determine the stability of the steady states of each system.
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PERROTTA, Antea. "Differential Formulation coupled to the Dirichlet-to-Neumann operator for scattering problems." Doctoral thesis, Università degli studi di Cassino, 2020. http://hdl.handle.net/11580/75845.

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This Thesis proposes the use of the Dirichlet-to-Neumann (DtN) operator to improve the accuracy and the efficiency of the numerical solution of an electromagnetic scattering problem, described in terms of a differential formulation. From a general perspective, the DtN operator provides the “connection” (the mapping) between the Dirichlet and the Neumann data onto a proper closed surface. This allows truncation of the computational domain when treating a scattering problem in an unbounded media. Moreover, the DtN operator provides an exact boundary condition, in contrast to other methods such as Perfectly Matching Layer (PML) or Absorbing Boundary Conditions (ABC). In addition, when the surface where the DtN is introduced has a canonical shape, as in the present contribution, the DtN operator can be computed analytically. This thesis is focused on a 2D geometry under TM illumination. The numerical model combines a differential formulation with the DtN operator defined onto a canonical surface where it can be computed analytically. Test cases demonstrate the accuracy and the computational advantage of the proposed technique.
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Marco, Alacid Onofre. "Structural Shape Optimization Based On The Use Of Cartesian Grids." Doctoral thesis, Universitat Politècnica de València, 2018. http://hdl.handle.net/10251/86195.

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As ever more challenging designs are required in present-day industries, the traditional trial-and-error procedure frequently used for designing mechanical parts slows down the design process and yields suboptimal designs, so that new approaches are needed to obtain a competitive advantage. With the ascent of the Finite Element Method (FEM) in the engineering community in the 1970s, structural shape optimization arose as a promising area of application. However, due to the iterative nature of shape optimization processes, the handling of large quantities of numerical models along with the approximated character of numerical methods may even dissuade the use of these techniques (or fail to exploit their full potential) because the development time of new products is becoming ever shorter. This Thesis is concerned with the formulation of a 3D methodology based on the Cartesian-grid Finite Element Method (cgFEM) as a tool for efficient and robust numerical analysis. This methodology belongs to the category of embedded (or fictitious) domain discretization techniques in which the key concept is to extend the structural analysis problem to an easy-to-mesh approximation domain that encloses the physical domain boundary. The use of Cartesian grids provides a natural platform for structural shape optimization because the numerical domain is separated from a physical model, which can easily be changed during the optimization procedure without altering the background discretization. Another advantage is the fact that mesh generation becomes a trivial task since the discretization of the numerical domain and its manipulation, in combination with an efficient hierarchical data structure, can be exploited to save computational effort. However, these advantages are challenged by several numerical issues. Basically, the computational effort has moved from the use of expensive meshing algorithms towards the use of, for example, elaborate numerical integration schemes designed to capture the mismatch between the geometrical domain boundary and the embedding finite element mesh. To do this we used a stabilized formulation to impose boundary conditions and developed novel techniques to be able to capture the exact boundary representation of the models. To complete the implementation of a structural shape optimization method an adjunct formulation is used for the differentiation of the design sensitivities required for gradient-based algorithms. The derivatives are not only the variables required for the process, but also compose a powerful tool for projecting information between different designs, or even projecting the information to create h-adapted meshes without going through a full h-adaptive refinement process. The proposed improvements are reflected in the numerical examples included in this Thesis. These analyses clearly show the improved behavior of the cgFEM technology as regards numerical accuracy and computational efficiency, and consequently the suitability of the cgFEM approach for shape optimization or contact problems.
La competitividad en la industria actual impone la necesidad de generar nuevos y mejores diseños. El tradicional procedimiento de prueba y error, usado a menudo para el diseño de componentes mecánicos, ralentiza el proceso de diseño y produce diseños subóptimos, por lo que se necesitan nuevos enfoques para obtener una ventaja competitiva. Con el desarrollo del Método de los Elementos Finitos (MEF) en el campo de la ingeniería en la década de 1970, la optimización de forma estructural surgió como un área de aplicación prometedora. El entorno industrial cada vez más exigente implica ciclos cada vez más cortos de desarrollo de nuevos productos. Por tanto, la naturaleza iterativa de los procesos de optimización de forma, que supone el análisis de gran cantidad de geometrías (para las se han de usar modelos numéricos de gran tamaño a fin de limitar el efecto de los errores intrínsecamente asociados a las técnicas numéricas), puede incluso disuadir del uso de estas técnicas. Esta Tesis se centra en la formulación de una metodología 3D basada en el Cartesian-grid Finite Element Method (cgFEM) como herramienta para un análisis numérico eficiente y robusto. Esta metodología pertenece a la categoría de técnicas de discretización Immersed Boundary donde el concepto clave es extender el problema de análisis estructural a un dominio de aproximación, que contiene la frontera del dominio físico, cuya discretización (mallado) resulte sencilla. El uso de mallados cartesianos proporciona una plataforma natural para la optimización de forma estructural porque el dominio numérico está separado del modelo físico, que podrá cambiar libremente durante el procedimiento de optimización sin alterar la discretización subyacente. Otro argumento positivo reside en el hecho de que la generación de malla se convierte en una tarea trivial. La discretización del dominio numérico y su manipulación, en coalición con la eficiencia de una estructura jerárquica de datos, pueden ser explotados para ahorrar coste computacional. Sin embargo, estas ventajas pueden ser cuestionadas por varios problemas numéricos. Básicamente, el esfuerzo computacional se ha desplazado. Del uso de costosos algoritmos de mallado nos movemos hacia el uso de, por ejemplo, esquemas de integración numérica elaborados para poder capturar la discrepancia entre la frontera del dominio geométrico y la malla de elementos finitos que lo embebe. Para ello, utilizamos, por un lado, una formulación de estabilización para imponer condiciones de contorno y, por otro lado, hemos desarrollado nuevas técnicas para poder captar la representación exacta de los modelos geométricos. Para completar la implementación de un método de optimización de forma estructural se usa una formulación adjunta para derivar las sensibilidades de diseño requeridas por los algoritmos basados en gradiente. Las derivadas no son sólo variables requeridas para el proceso, sino una poderosa herramienta para poder proyectar información entre diferentes diseños o, incluso, proyectar la información para crear mallas h-adaptadas sin pasar por un proceso completo de refinamiento h-adaptativo. Las mejoras propuestas se reflejan en los ejemplos numéricos presentados en esta Tesis. Estos análisis muestran claramente el comportamiento superior de la tecnología cgFEM en cuanto a precisión numérica y eficiencia computacional. En consecuencia, el enfoque cgFEM se postula como una herramienta adecuada para la optimización de forma.
Actualment, amb la competència existent en la industria, s'imposa la necessitat de generar nous i millors dissenys . El tradicional procediment de prova i error, que amb freqüència es fa servir pel disseny de components mecànics, endarrereix el procés de disseny i produeix dissenys subòptims, pel que es necessiten nous enfocaments per obtindre avantatge competitiu. Amb el desenvolupament del Mètode dels Elements Finits (MEF) en el camp de l'enginyeria en la dècada de 1970, l'optimització de forma estructural va sorgir com un àrea d'aplicació prometedora. No obstant això, a causa de la natura iterativa dels processos d'optimització de forma, la manipulació dels models numèrics en grans quantitats, junt amb l'error de discretització dels mètodes numèrics, pot fins i tot dissuadir de l'ús d'aquestes tècniques (o d'explotar tot el seu potencial), perquè al mateix temps els cicles de desenvolupament de nous productes s'estan acurtant. Esta Tesi se centra en la formulació d'una metodologia 3D basada en el Cartesian-grid Finite Element Method (cgFEM) com a ferramenta per una anàlisi numèrica eficient i sòlida. Esta metodologia pertany a la categoria de tècniques de discretització Immersed Boundary on el concepte clau és expandir el problema d'anàlisi estructural a un domini d'aproximació fàcil de mallar que conté la frontera del domini físic. L'utilització de mallats cartesians proporciona una plataforma natural per l'optimització de forma estructural perquè el domini numèric està separat del model físic, que podria canviar lliurement durant el procediment d'optimització sense alterar la discretització subjacent. A més, un altre argument positiu el trobem en què la generació de malla es converteix en una tasca trivial, ja que la discretització del domini numèric i la seua manipulació, en coalició amb l'eficiència d'una estructura jeràrquica de dades, poden ser explotats per estalviar cost computacional. Tot i això, estos avantatges poden ser qüestionats per diversos problemes numèrics. Bàsicament, l'esforç computacional s'ha desplaçat. De l'ús de costosos algoritmes de mallat ens movem cap a l'ús de, per exemple, esquemes d'integració numèrica elaborats per poder capturar la discrepància entre la frontera del domini geomètric i la malla d'elements finits que ho embeu. Per això, fem ús, d'una banda, d'una formulació d'estabilització per imposar condicions de contorn i, d'un altra, desevolupem noves tècniques per poder captar la representació exacta dels models geomètrics Per completar la implementació d'un mètode d'optimització de forma estructural es fa ús d'una formulació adjunta per derivar les sensibilitats de disseny requerides pels algoritmes basats en gradient. Les derivades no són únicament variables requerides pel procés, sinó una poderosa ferramenta per poder projectar informació entre diferents dissenys o, fins i tot, projectar la informació per crear malles h-adaptades sense passar per un procés complet de refinament h-adaptatiu. Les millores proposades s'evidencien en els exemples numèrics presentats en esta Tesi. Estes anàlisis mostren clarament el comportament superior de la tecnologia cgFEM en tant a precisió numèrica i eficiència computacional. Així, l'enfocament cgFEM es postula com una ferramenta adient per l'optimització de forma.
Marco Alacid, O. (2017). Structural Shape Optimization Based On The Use Of Cartesian Grids [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/86195
TESIS
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Coco, Armando. "Finite-Difference Ghost-Cell Multigrid Methods for Elliptic problems with Mixed Boundary Conditions and Discontinuous Coefficients." Doctoral thesis, Università di Catania, 2012. http://hdl.handle.net/10761/1107.

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The work of this thesis is devoted to the development of an original and general numerical method for solving the elliptic equation in an arbitrary domain (described by a level-set function) with general boundary conditions (Dirichlet, Neumann, Robin, ...) using Cartesian grids. It can be then considered an immersed boundary method, and the scheme we use is based on a finite-difference ghost-cell technique. The entire problem is solved by an effective multigrid solver, whose components have been suitably constructed in order to be applied to the scheme. The method is extended to the more challenging case of discontinuous coefficients, and the multigrid is suitable modified in order to attain the optimal convergence factor of the whole iteration procedure. The development of the multigrid is an important feature of this thesis, since multigrid solvers for discontinuous coefficients maintaining the optimal convergence factor without depending on the jump in the coefficient and on the problem size is recently studied in literature. The method is second order accurate in the solution and its gradient. A convergence proof for the first order scheme is provided, while second order is confirmed by several numerical tests.
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Eschke, Andy. "Analytical solution of a linear, elliptic, inhomogeneous partial differential equation with inhomogeneous mixed Dirichlet- and Neumann-type boundary conditions for a special rotationally symmetric problem of linear elasticity." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-149965.

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The analytical solution of a given inhomogeneous boundary value problem of a linear, elliptic, inhomogeneous partial differential equation and a set of inhomogeneous mixed Dirichlet- and Neumann-type boundary conditions is derived in the present paper. In the context of elasticity theory, the problem arises for a non-conservative symmetric ansatz and an extended constitutive law shown earlier. For convenient user application, the scalar function expressed in cylindrical coordinates is primarily obtained for the general case before being expatiated on a special case of linear boundary conditions.
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Junior, Vanderley Alves Ferreira. "Problemas de valores de contorno envolvendo o operador biharmônico." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-20032013-083331/.

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Estudamos o problema de valores de contorno {\'DELTA POT. 2\' u = f em \'OMEGA\', \'BETA\' u = 0 em \'PARTIAL OMEGA\', um aberto limitado \'OMEGA\' \'ESTÁ CONTIDO\' \'R POT. N\' , sob diferentes condições de contorno. As questões de existência e positividade de soluções para este problema são abordadas com condições de contorno de Dirichlet, Navier e Steklov. Deduzimos condições de contorno naturais através do estudo de um modelo para uma placa com carga estática. Estudamos ainda propriedades do primeiro autovalor de \'DELTA POT. 2\' e o problema semilinear {\'DELTA POT. 2\' u = F (u) em \'OMEGA\' u = \'PARTIAL\'u SUP . \'PARTIAL\' v = 0 em \'PARTIUAL\' \'OMEGA\', para não-linearidades do tipo F(t) = \'l t l POT. p-1\', p \' DIFERENTE\' t, p > 0. Para tal problema estudamos existência e não-existência de soluções e positividade
We study the boundary value problem {\'DELTA POT. 2\' u = f in \'OMEGA\', \'BETA\' u = 0 in \'PARTIAL OMEGA\', in a bounded open \'OMEGA\'\'THIS CONTAINED\' \'R POT. N\' , under different boundary conditions. The questions of existence and positivity of solutions for this problem are addressed with Dirichlet, Navier and Steklov boundary conditions. We deduce natural boundary conditions through the study of a model for a plate with static load. We also study properties of the first eigenvalue of \'DELTA POT. 2\' and the semi-linear problem { \'DELTA POT. 2\' e o problema semilinear {\'DELTA POT. 2\' u = F (u) in \'OMEGA\' u = \'PARTIAL\'u SUP . \'PARTIAL\' v = 0 in \'PARTIUAL\' \'OMEGA\', for non-linearities like F(t) = \'l t l POT. p-1\', p \' DIFFERENT\' t, p > 0. For such problem we study existence and non-existence of solutions and its positivity
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Books on the topic "Dirichlet boundary condition"

1

J, Liandrat, and Institute for Computer Applications in Science and Engineering., eds. On the effective construction of compactly supported wavelets satisfying homogenous boundary conditions on the interval. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1996.

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Adi, Ditkowski, and Institute for Computer Applications in Science and Engineering., eds. Multi-dimensional asymptotically stable 4th order accurate schemes for the diffusion equation. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1996.

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Adi, Ditkowski, and Institute for Computer Applications in Science and Engineering., eds. Multi-dimensional asymptotically stable 4th order accurate schemes for the diffusion equation. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1996.

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Adi, Ditkowski, and Institute for Computer Applications in Science and Engineering., eds. Multi-dimensional asymptotically stable 4th order accurate schemes for the diffusion equation. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1996.

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Mann, Peter. The Stationary Action Principle. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0007.

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This crucial chapter focuses on the stationary action principle. It introduces Lagrangian mechanics, using first-order variational calculus to derive the Euler–Lagrange equation, and the inverse problem is described. The chapter then considers the Ostrogradsky equation and discusses the properties of the extrema using the second-order variation to the action. It then discusses the difference between action functions (of Dirichlet boundary conditions) and action functionals of the extremal path. The different types of boundary conditions (Dirichlet vs Neumann) are elucidated. Topics discussed include Hessian conditions, Douglas’s theorem, the Jacobi last multiplier, Helmholtz conditions, Noether-type variation and Frenet–Serret frames, as well as concepts such as on shell and off shell. Actions of non-continuous extremals are examined using Weierstrass–Erdmann corner conditions, and the action principle is written in the most general form as the Hamilton–Suslov principle. Important applications of the Euler–Lagrange formulation are highlighted, including protein folding.
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Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I: Dirichlet Boundary Conditions on Euclidean Space. Springer International Publishing AG, 2022.

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Multi-dimensional asymptotically stable 4th order accurate schemes for the diffusion equation. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1996.

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Bounded error schemes for the wave equation on complex domains. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.

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Edmunds, D. E., and W. D. Evans. Second-Order Differential Operators on Arbitrary Open Sets. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0007.

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In this chapter, three different methods are described for obtaining nice operators generated in some L2 space by second-order differential expressions and either Dirichlet or Neumann boundary conditions. The first is based on sesquilinear forms and the determination of m-sectorial operators by Kato’s First Representation Theorem; the second produces an m-accretive realization by a technique due to Kato using his distributional inequality; the third has its roots in the work of Levinson and Titchmarsh and gives operators T that are such that iT is m-accretive. The class of such operators includes the self-adjoint operators, even ones that are not bounded below. The essential self-adjointness of Schrödinger operators whose potentials have strong local singularities are considered, and the quantum-mechanical interpretation of essential self-adjointness is discussed.
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Book chapters on the topic "Dirichlet boundary condition"

1

Bianchi, Massimo, Roland Allen, Antonio Mondragon, Alexander Gavrilik, John Howie, Martin Schlichenmaier, Martin Schlichenmaier, et al. "Dirichlet-Neumann Boundary Condition." In Concise Encyclopedia of Supersymmetry, 130. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/1-4020-4522-0_162.

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Motreanu, Dumitru, and Zdzisław Naniewicz. "Semilinear Hemivariational Inequalities with Dirichlet Boundary Condition." In Advances in Mechanics and Mathematics, 89–110. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/978-1-4757-4435-4_2.

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Grote, Marcus J., and Christoph Kirsch. "Dirichlet-to-Neumann Boundary Condition for Multiple Scattering Problems." In Mathematical and Numerical Aspects of Wave Propagation WAVES 2003, 263–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55856-6_42.

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Piasecki, Tomasz, and Milan Pokorný. "Steady Compressible Navier–Stokes–Fourier System with Slip Boundary Condition for the Velocity and Dirichlet Boundary Condition for the Temperature." In Fluids Under Control, 217–39. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-27625-5_8.

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Pokorný, Milan. "Steady Compressible Navier–Stokes–Fourier Equations with Dirichlet Boundary Condition for the Temperature." In Collected Papers in Honor of Yoshihiro Shibata, 335–50. Cham: Springer Nature Switzerland, 2022. http://dx.doi.org/10.1007/978-3-031-19252-4_14.

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Schmitz, Hermann. "A collocation method for potential problems with a mixed Dirichlet-Signorini boundary condition." In Teubner-Texte zur Mathematik, 194–200. Wiesbaden: Vieweg+Teubner Verlag, 1992. http://dx.doi.org/10.1007/978-3-663-11577-9_20.

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Ezhak, Svetlana. "On Estimates for the First Eigenvalue of the Sturm–Liouville Problem with Dirichlet Boundary Conditions and Integral Condition." In Differential and Difference Equations with Applications, 387–94. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7333-6_32.

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Droniou, Jérôme, Robert Eymard, Thierry Gallouët, Cindy Guichard, and Raphaèle Herbin. "Dirichlet Boundary Conditions." In Mathématiques et Applications, 17–65. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-79042-8_2.

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Feltrin, Guglielmo. "Dirichlet Boundary Conditions." In Positive Solutions to Indefinite Problems, 3–37. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94238-4_1.

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Motreanu, Dumitru, Viorica Venera Motreanu, and Nikolaos Papageorgiou. "Nonlinear Elliptic Equations with Dirichlet Boundary Conditions." In Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems, 303–85. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-9323-5_11.

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Conference papers on the topic "Dirichlet boundary condition"

1

Qiaoling Jiang, Weige Wu, and Jianxin Liu. "Monte Carlo method for Dirichlet boundary condition of multimedia field." In 2009 International Conference on Microwave Technology and Computational Electromagnetics (ICMTCE 2009). IET, 2009. http://dx.doi.org/10.1049/cp.2009.1356.

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Ashyralyev, Allaberen, Kadriye Tuba Turkcan, and Mehmet Emir Koksal. "Numerical solutions of telegraph equations with the Dirichlet boundary condition." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4959669.

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Yusop, Nur Syaza Mohd, and Nurul Akmal Mohamed. "The system of equations for mixed BVP with one Dirichlet boundary condition and three Neumann boundary conditions." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON EDUCATION, MATHEMATICS AND SCIENCE 2016 (ICEMS2016) IN CONJUNCTION WITH 4TH INTERNATIONAL POSTGRADUATE CONFERENCE ON SCIENCE AND MATHEMATICS 2016 (IPCSM2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4983857.

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Yao, Guangfa. "A Simple Immersed Boundary Method for Modeling Forced Convection Heat Transfer." In ASME 2019 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/imece2019-10236.

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Abstract As non-body conforming numerical methods using simple Cartesian mesh, immersed boundary methods have become increasingly popular in modeling fluid-solid interaction. They usually do this by adding a body force term in the momentum equation. The magnitude and direction of this body force ensure that the boundary condition on the solid-fluid interface is satisfied without invoking complicated body-conforming numerical methods to impose the boundary condition. A similar path has been followed to model forced convection heat transfer by adding a source term in the energy equation. The added source term will ensure that thermal boundary conditions on the solid-fluid interface are imposed without invoking a boundary conforming mesh. These approaches were developed to handle the Dirichlet boundary condition (constant wall temperature). Few of them deal with the Neumann boundary condition (constant wall heat flux). This paper presents a simple new immersed boundary method. It can deal with the Dirichlet boundary condition, Neumann boundary condition and conjugated heat transfer by adding an energy source or sink term in the energy conservation equation. The presented approach is validated against the analytical solutions and a very good match is achieved.
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Jablonski, Pawel. "Approaches to mixed Dirichlet-Neumann boundary condition in the method of separation of variables." In 2019 Applications of Electromagnetics in Modern Techniques and Medicine (PTZE). IEEE, 2019. http://dx.doi.org/10.23919/ptze.2019.8781727.

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Junhong, Liu, Liu Wenxue, Li Lifeng, and Jin Qi. "Oscillation criteria for a class of nonlinear impulsive parabolic system under Dirichlet boundary condition." In 2015 International Conference on Advanced Mechatronic Systems (ICAMechS). IEEE, 2015. http://dx.doi.org/10.1109/icamechs.2015.7287129.

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Danarwindu, Ghiffari Ahnaf, and Nikenasih Binatari. "Green's function for convection diffusion equation with Dirichlet boundary condition using separation variable's method." In PROCEEDINGS OF THE 4TH INTERNATIONAL SEMINAR ON INNOVATION IN MATHEMATICS AND MATHEMATICS EDUCATION (ISIMMED) 2020: Rethinking the role of statistics, mathematics and mathematics education in society 5.0: Theory, research, and practice. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0108795.

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Surmont, Florian, and Damien Coache. "Investigation on the Shooting Method Ability to Solve Different Mooring Lines Boundary Condition Types." In ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/omae2018-77563.

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The study of undersea cables and mooring lines statics remains an unavoidable subject of simulation in offshore field for either steady-state analysis or dynamic simulation initialization. Whether the study concerns mooring systems pinned both at seabed and floating platform, cables towed by a moving underwater system or when special links such as stiffeners are needed, the ability to model every combination is a key point. To do so the authors propose to investigate the use of the shooting method to solve the two point boundary value problem (TPBVP) associated with Dirichlet, Robin or mixed boundary conditions representing respectively, displacement, force and force/displacement boundary conditions. 3D nonlinear static string calculations are confronted to a semi-analytic formulation established from the catenary closed form equations. The comparisons are performed on various pairs of boundary conditions developed in five configurations.
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Ahmad, Muhammad Jalil, and Korhan Günel. "Numerical Solution of Dirichlet Boundary Value Problems using Mesh Adaptive Direct Search Optimization." In International Students Science Congress. Izmir International Guest Student Association, 2021. http://dx.doi.org/10.52460/issc.2021.030.

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This study gives a different numerical approach for solving second order differential equation with a Dirichlet boundary condition. Mesh Adaptive Direct Search (MADS) algorithm is adopted to train the feed forward neural network used in this approach. As MADS is a derivative-free optimization algorithm, it helps us to reduce the time-consuming workload in the training stage. The results obtained from this approach are also compared with Generalized Pattern Search (GPS) algorithm.
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Atassi, Hafiz M., and Romeo F. Susan-Resiga. "Parallel Computation of Harmonic Waves Using Domain Decomposition: Part 1 — General Formulation." In ASME 1998 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/imece1998-0532.

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Abstract A method is presented for parallel computation of time-harmonic waves using an iterative scheme based on domain decomposition. For exterior radiation and scattering problems, a finite computational domain is obtained by introducing a computational outer boundary on which a modified Dirichlet-to-Neumann map is used as a nonreflecting condition. The computational domain is then decomposed into subdomains and for each a boundary-value problem is defined using impedance-like transmission conditions on the subdomain interfaces. An iterative scheme updates the subdomain boundary conditions so that a global continuous solution is recovered.
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Reports on the topic "Dirichlet boundary condition"

1

Babuska, Ivo, Victor Nistor, and Nicolae Tarfulea. Approximate Dirichlet Boundary Conditions in the Generalized Finite Element Method (PREPRINT). Fort Belvoir, VA: Defense Technical Information Center, February 2006. http://dx.doi.org/10.21236/ada478502.

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Babuska, Ivo, B. Guo, and Manil Suri. Implementation of Nonhomogeneous Dirichlet Boundary Conditions in the p- Version of the Finite Element Method. Fort Belvoir, VA: Defense Technical Information Center, September 1988. http://dx.doi.org/10.21236/ada207799.

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