Relevant bibliographies by topics / Multiscale problems

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Multiscale problems'

Author: Grafiati
Published: 13 April 2024

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Journal articles on the topic "Multiscale problems"

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Cohen, Albert, Wolfgang Dahmen, Ronald DeVore, and Angela Kunoth. "Multiscale and High-Dimensional Problems." Oberwolfach Reports 10, no. 3 (2013): 2179–257. http://dx.doi.org/10.4171/owr/2013/39.

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Cohen, Albert, Wolfgang Dahmen, Ronald DeVore, and Angela Kunoth. "Multiscale and High-Dimensional Problems." Oberwolfach Reports 14, no. 1 (January 2, 2018): 1001–51. http://dx.doi.org/10.4171/owr/2017/17.

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WIJESEKERA, NIMAL, GUOGANG FENG, and THOMAS L. BECK. "MULTISCALE ALGORITHMS FOR EIGENVALUE PROBLEMS." Journal of Theoretical and Computational Chemistry 02, no. 04 (December 2003): 553–61. http://dx.doi.org/10.1142/s0219633603000665.

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Iterative multiscale methods for electronic structure calculations offer several advantages for large-scale problems. Here we examine a nonlinear full approximation scheme (FAS) multigrid method for solving fixed potential and self-consistent eigenvalue problems. In principle, the expensive orthogonalization and Ritz projection operations can be moved to coarse levels, thus substantially reducing the overall computational expense. Results of the nonlinear multiscale approach are presented for simple fixed potential problems and for self-consistent pseudopotential calculations on large molecules. It is shown that, while excellent efficiencies can be obtained for problems with small numbers of states or well-defined eigenvalue cluster structure, the algorithm in its original form stalls for large-molecule problems with tens of occupied levels. Work is in progress to attempt to alleviate those difficulties.
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Hyman, J. M. "Patch Dynamics for Multiscale Problems." Computing in Science and Engineering 7, no. 3 (May 2005): 47–53. http://dx.doi.org/10.1109/mcse.2005.57.

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Målqvist, Axel. "Multiscale Methods for Elliptic Problems." Multiscale Modeling & Simulation 9, no. 3 (July 2011): 1064–86. http://dx.doi.org/10.1137/090775592.

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Proksch, Katharina, Frank Werner, and Axel Munk. "Multiscale scanning in inverse problems." Annals of Statistics 46, no. 6B (December 2018): 3569–602. http://dx.doi.org/10.1214/17-aos1669.

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Målqvist, Axel, and Daniel Peterseim. "Localization of elliptic multiscale problems." Mathematics of Computation 83, no. 290 (June 16, 2014): 2583–603. http://dx.doi.org/10.1090/s0025-5718-2014-02868-8.

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Kickinger, Ferdinand. "Multiscale Problems; Meshes and Solvers." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 78, S3 (1998): 963–64. http://dx.doi.org/10.1002/zamm.19980781552.

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Masud, Arif, and Leopoldo P. Franca. "A hierarchical multiscale framework for problems with multiscale source terms." Computer Methods in Applied Mechanics and Engineering 197, no. 33-40 (June 2008): 2692–700. http://dx.doi.org/10.1016/j.cma.2007.12.024.

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Song, Fei, and Weibing Deng. "Multiscale discontinuous Petrov-Galerkin method for the multiscale elliptic problems." Numerical Methods for Partial Differential Equations 34, no. 1 (August 16, 2017): 184–210. http://dx.doi.org/10.1002/num.22191.

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Dissertations / Theses on the topic "Multiscale problems"

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Miller, Mark Andrew. "Multiscale techniques for imaging problems." Thesis, University of Cambridge, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.613033.

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Holst, Henrik. "Multiscale Methods for Wave Propagation Problems." Doctoral thesis, KTH, Numerisk analys, NA, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-48072.

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Simulations of wave propagation in heterogeneous media and at high frequencies are important in many applications such as seismic-, {electro-magnetic-,} acoustic-, fluid flow problems and others. These are classical multiscale problems and often too computationally expensive for direct numerical simulation. The smallest scales must be well resolved over a computational domain represented by the largest scale and this results in a very high computational cost. We develop and analyze numerical techniques based on the heterogeneous multiscale method (HMM) framework for such wave equations with highly oscillatory solutions $u^{\varepsilon}$ where $\varepsilon$ represents the size of the smallest scale. In these techniques the oscillatory microscale is approximated on small local microproblems of size $\varepsilon$ in spatial and time directions. The solution of the microproblems are then coupled to a global macroscale model in divergence form $u_{tt} = \nabla \cdot F$ where the flux $F$ is obtained from the microproblems. The oscillations can either originate from fluctuations in the velocity coefficients or from high frequency initial and boundary conditions. We have developed algorithms that couple micro and macroscales for both these cases. The choice of macroscale variables is inspired by the analytic theories of homogenization and geometrical optics respectively. In the first case local averages $u \approx u^{\varepsilon}$ are used on the macroscale. In the second case, phase $\phi$ and energy are natural macroscopic variables. There are two major goals of this research. One goal is to develop and analyze algorithms for simulating multiscale wave propagation with low computational complexity, and even independent of $\varepsilon$ for finite time problems. This is seen in many examples in one, two and three dimensions. The other goal is to use wave propagation as a model to better understand the HMM framework. An example in this direction is simulation with oscillatory wave field over long time. The dispersive effects that then occur is well approximated by a HMM method that was originally formulated for finite time where added accuracy is required but no explicit adjustment to include dispersion, an evidence of the robustness of the method.
Simulering av högfrekventa vågor i heterogena material är viktigt i många tillämpningar, till exempel seismologi, elektromagnetism, akustik och  strömningsmekanik. Dessa tillämpningar är exempel på klassiska multiskalproblem och har typiskt en för hög beräkningskostnad, i form av datortid och minne, för en direkt numerisk simulering. De minsta skalorna i problemet måste vara upplösta över ett område som representeras av dom största skalorna och detta innebär en hög beräkningskostnad. Vi har utvecklat och analyserat numeriska metoder för vågekvationer med snabbt oscillerande lösningar $u^{\varepsilon}$ där $\varepsilon$ representerar storleken på den minsta skalan. Metoderna är baserade på ramverket \emph{heterogena multiskalmetoden} (HMM). I dessa metoder approximeras den hastigt oscillerande mikroskalan med små lokala mikroproblem av storleksordning $\varepsilon$ i tids- och rumsriktning. Lösningen till mikroproblemen är kopplade till en global modell på makroskalan i divergensform $u_{tt} = \nabla \cdot F$, där flödet $F$ ges av mikroproblemen. De hastiga oscillationerna kan härröras från snabba variationer i hastighetsfältet, begynnelsevillkor eller randvillkor. Vi har utvecklat algoritmer som kopplar mikro- och makroskalor i bägge fallen. Valet av makroskalvariabler inspireras av de analytiska metoderna homogenisering och geometrisk optik. I det första fallet används lokala medelvärden $u \approx u^{\varepsilon}$ på makroskalnivån. I det andra fallet är fas $\phi$ och energi bra val av makroskalvariabler. Det finns två huvudmål med vår forskning. Ett mål är att utveckla och analysera algoritmer för simulering av vågproblem med multipla skalor med låg beräkningskostnad (om möjligt, oberoende av $\varepsilon$) för problem över begränsad tid. Vi visar numeriska resultat från multiskalproblem i en, två och tre dimensioner. Det andra målet är att att använda vågutbredning som en modell för att bättre förstå HMM ramverket. Ett exempel på detta är simulering med oscillerande hastighetsfält över lång tid. Efter lång tid så uppträder dispersion. Vi har demonstrerat att vår HMM-metod, som ursprungligen var formulerad för begränsad tid, även kan appliceras på detta fall. För att få den rätta dispersionen krävs högre noggrannhetsordning, men metoden ändrar inte form. Detta visar på metodens robusthet.
QC 20111117
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Söderlund, Robert. "Finite element methods for multiscale/multiphysics problems." Doctoral thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-42713.

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In this thesis we focus on multiscale and multiphysics problems. We derive a posteriori error estimates for a one way coupled multiphysics problem, using the dual weighted residual method. Such estimates can be used to drive local mesh refinement in adaptive algorithms, in order to efficiently obtain good accuracy in a desired goal quantity, which we demonstrate numerically. Furthermore we prove existence and uniqueness of finite element solutions for a two way coupled multiphysics problem. The possibility of deriving dual weighted a posteriori error estimates for two way coupled problems is also addressed. For a two way coupled linear problem, we show numerically that unless the coupling of the equations is to strong the propagation of errors between the solvers goes to zero. We also apply a variational multiscale method to both an elliptic and a hyperbolic problem that exhibits multiscale features. The method is based on numerical solutions of decoupled local fine scale problems on patches. For the elliptic problem we derive an a posteriori error estimate and use an adaptive algorithm to automatically tune the resolution and patch size of the local problems. For the hyperbolic problem we demonstrate the importance of how to construct the patches of the local problems, by numerically comparing the results obtained for symmetric and directed patches.
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Elfverson, Daniel. "Discontinuous Galerkin Multiscale Methods for Elliptic Problems." Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-138960.

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In this paper a continuous Galerkin multiscale method (CGMM) and a discontinuous Galerkin multiscale method (DGMM) are proposed, both based on the variational multiscale method for solving partial differential equations numerically. The solution is decoupled into a coarse and a fine scale contribution, where the fine-scale contribution is computed on patches with localized right hand side. Numerical experiments are presented where exponential decay of the error is observed when increasing the size of the patches for both CGMM and DGMM. DGMM gives much better accuracy when the same size of the patches are used.
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Savchuk, Tatyana. "The multiscale finite element method for elliptic problems." Ann Arbor, Mich. : ProQuest, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3245025.

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Thesis (Ph. D. in Applied Mathematics)--Southern Methodist University, 2007.
Title from PDF title page (viewed Mar. 18, 2008). Source: Dissertation Abstracts International, Volume: 67-12, Section: B, page: 7120. Adviser: Zhangxin (John) Chen. Includes bibliographical references.
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Kudreyko, Aleksey. "Multiscale wavelet analysis for integral and differential problems." Doctoral thesis, Universita degli studi di Salerno, 2011. http://hdl.handle.net/10556/176.

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2009 - 2010
The object of the present research is wavelet analysis of integral and differential problems by means of harmonic and circular wavelets. It is shown that circular wavelets constitute a complete basis for L2[0; 1] functions, and form multiresolution analysis. Multiresolution analysis can be briefly considered as a decomposition of L2[0; 1] into a complete set of scale depending subspaces of wavelets. Thus, integral operators, differential operators, and L2(R) functions were investigated as scale depending functions through their projection onto these subspaces of wavelets. In particular: - conditions when a certain wavelet can be applied for solution of integral or differential problem are given; - it is shown that the accuracy of this approach exponentially grows when increasing the number of vanishing moments and scaling parameter; - wavelet solutions of low-dimensional nonlinear partial differential equations are compared with other methods; - wavelet-based approach is applied to low-dimensional Fredholm integral equations and the Galerkin method for two-dimensional Fredholm integral equations.[edited by author]. Oggetto della seguente ricerca `e l’analisi di problemi differenziali e integrali, utilizzando wavelet armoniche e wavelet armoniche periodiche. Si dimostra che le wavelet periodiche costituiscono una base completa per le funzioni L2[0; 1] e formano un’analisi multiscala. L’analisi multirisoluzione pu`o essere brevemente considerata come la decomposizione di L2[0; 1] in un insieme completo di sottospazi di wavelet dipendenti da un fattore di scala. Pertanto gli operatori integrali e differenziali e le funzioni L2(R) vengono studiati come funzioni di scala mediante le corrispondenti proiezioni in questi sottospazi di wavelet. In particolare, vengono sviluppati quattro principali argomenti: - sono state individuate le condizioni per applicare una data famiglia di wavelets alla soluzione di un data problema differenziale o integrale; - si `e dimostrato che la precisione di questo approccio cresce esponenzialmente quando decresce il numero dei momenti nulli e del parametro di scala; - soluzioni wavelet di equazioni differenziali a derivate parziali nonlineari di dimensione bassa sono state confrontate con altri metodi di soluzioni; - l’approccio basato sull’uso delle wavelet `e stato applicato anche per ricerca di soluzioni di alcune equazioni integrali di Fredholm e insieme al metodo di Galerkin per risolvere equazioni integrali Fredholm di dimensioni due.[a cura dell'autore]
IX n.s.
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Hellman, Fredrik. "Multiscale and multilevel methods for porous media flow problems." Licentiate thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-262276.

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We consider two problems encountered in simulation of fluid flow through porous media. In macroscopic models based on Darcy's law, the permeability field appears as data. The first problem is that the permeability field generally is not entirely known. We consider forward propagation of uncertainty from the permeability field to a quantity of interest. We focus on computing p-quantiles and failure probabilities of the quantity of interest. We propose and analyze improved standard and multilevel Monte Carlo methods that use computable error bounds for the quantity of interest. We show that substantial reductions in computational costs are possible by the proposed approaches. The second problem is fine scale variations of the permeability field. The permeability often varies on a scale much smaller than that of the computational domain. For standard discretization methods, these fine scale variations need to be resolved by the mesh for the methods to yield accurate solutions. We analyze and prove convergence of a multiscale method based on the Raviart–Thomas finite element. In this approach, a low-dimensional multiscale space based on a coarse mesh is constructed from a set of independent fine scale patch problems. The low-dimensional space can be used to yield accurate solutions without resolving the fine scale.
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Parno, Matthew David. "A multiscale framework for Bayesian inference in elliptic problems." Thesis, Massachusetts Institute of Technology, 2011. http://hdl.handle.net/1721.1/65322.

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Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2011.
Page 118 blank. Cataloged from PDF version of thesis.
Includes bibliographical references (p. 112-117).
The Bayesian approach to inference problems provides a systematic way of updating prior knowledge with data. A likelihood function involving a forward model of the problem is used to incorporate data into a posterior distribution. The standard method of sampling this distribution is Markov chain Monte Carlo which can become inefficient in high dimensions, wasting many evaluations of the likelihood function. In many applications the likelihood function involves the solution of a partial differential equation so the large number of evaluations required by Markov chain Monte Carlo can quickly become computationally intractable. This work aims to reduce the computational cost of sampling the posterior by introducing a multiscale framework for inference problems involving elliptic forward problems. Through the construction of a low dimensional prior on a coarse scale and the use of iterative conditioning technique the scales are decouples and efficient inference can proceed. This work considers nonlinear mappings from a fine scale to a coarse scale based on the Multiscale Finite Element Method. Permeability characterization is the primary focus but a discussion of other applications is also provided. After some theoretical justification, several test problems are shown that demonstrate the efficiency of the multiscale framework.
by Matthew David Parno.
S.M.
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Biezemans, Rutger. "Multiscale methods : non-intrusive implementation, advection-dominated problems and related topics." Electronic Thesis or Diss., Marne-la-vallée, ENPC, 2023. http://www.theses.fr/2023ENPC0029.

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Cette thèse porte sur les méthodes numériques pour les équations aux dérivées partielles (EDP) multi-échelles, et en particulier sur la méthode dite des éléments finis multi-échelles (MsFEM). Celle-ci est une méthode de type éléments finis qui consiste en une approximation de Galerkin de l'EDP sur une base problème-dépendante. Trois difficultés particulières liées à cette méthode sont abordées dans cette thèse. Premièrement, puisque la MsFEM utilise une base problème-dépendante, la méthode ne peut être facilement implémentée dans des codes industriels génériques. Cela freine la diffusion de la MsFEM au-delà des environnements académiques. Une méthodologie générique est proposée pour convertir la MsFEM en un problème effectif qui peut être résolu par des codes génériques. Il est démontré par des résultats théoriques ainsi que des expériences numériques que la nouvelle méthodologie est aussi précise que la MsFEM originale. Deuxièmement, les MsFEM adaptées aux problèmes advection-dominés sont étudiées. Ce régime spécifique rend instables les discrétisations naïves. Une explication est trouvée pour l'instabilité de certaines méthodes proposées précédemment. Des expériences numériques montrent la stabilité d'une MsFEM avec des conditions aux limites de type Crouzeix-Raviart enrichie par des fonctions bulles. Troisièmement, une nouvelle analyse de convergence pour la MsFEM est présentée, permettant pour la première fois d'établir la convergence sous des hypothèses de régularité minimales. Cette démarche est importante pour réduire l'écart entre la théorie pour la MsFEM et son application en pratique, où les hypothèses de régularité habituelles sont rarement satisfaites
This thesis is concerned with computational methods for multiscale partial differential equations (PDEs), and in particular the multiscale finite element method (MsFEM). This is a finite element type method that performs a Galerkin approximation of the PDE on a problem-dependent basis. Three particular difficulties related to the method are addressed in this thesis. First, the intrusiveness of the MsFEM is considered. Since the MsFEM uses a problem-dependent basis, it cannot easily be implemented in generic industrial codes and this hinders its adoption beyond academic environments. A generic methodology is proposed that translates the MsFEM into an effective problem that can be solved by generic codes. It is shown by theoretical convergence estimates and numerical experiments that the new methodology is as accurate as the original MsFEM. Second, MsFEMs for advection-dominated problems are studied. These problems cause additional instabilities for naive discretizations. An explanation is found for the instability of previously proposed methods. Numerical experiments show the stability of an MsFEM with Crouzeix-Raviart type boundary conditions enriched with bubble functions. Third, a new convergence analysis for the MsFEM is presented that, for the first time, establishes convergence under minimal regularity hypotheses. This bridges an important gap between the theoretical understanding of the method and its field of application, where the usual regularity hypotheses are rarely satisfied
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Litvinenko, Alexander [Verfasser]. "Application of hierarchical matrices for solving multiscale problems / Alexander Litvinenko." Aachen : Universitätsbibliothek der RWTH Aachen, 2019. http://d-nb.info/1193181313/34.

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Books on the topic "Multiscale problems"

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Graham, Ivan G., Thomas Y. Hou, Omar Lakkis, and Robert Scheichl, eds. Numerical Analysis of Multiscale Problems. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-22061-6.

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Symposium, LMS Durham, ed. Numerical analysis of multiscale problems. Heidelberg: Springer, 2012.

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Blanc, Xavier, and Claude Le Bris. Homogenization Theory for Multiscale Problems. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-21833-0.

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Antonić, Nenad, C. J. van Duijn, Willi Jäger, and Andro Mikelić, eds. Multiscale Problems in Science and Technology. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-56200-6.

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Banasiak, Jacek, Mark A. J. Chaplain, and Jacek Miękisz. Multiscale Problems in the Life Sciences. Edited by Vincenzo Capasso and Mirosław Lachowicz. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-78362-6.

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Madureira, Alexandre L. Numerical Methods and Analysis of Multiscale Problems. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-50866-5.

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Bramble, James H., Albert Cohen, and Wolfgang Dahmen. Multiscale Problems and Methods in Numerical Simulations. Edited by Claudio Canuto. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/b13466.

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From multiscale modeling to metamodeling of geomechanics problems. [New York, N.Y.?]: [publisher not identified], 2019.

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Eberhard, Peter, ed. IUTAM Symposium on Multiscale Problems in Multibody System Contacts. Dordrecht: Springer Netherlands, 2007. http://dx.doi.org/10.1007/978-1-4020-5981-0.

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Axel, Voigt, ed. Multiscale modeling in epitaxial growth. Basel: Birkhäuser, 2005.

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Book chapters on the topic "Multiscale problems"

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Pechstein, Clemens. "Multiscale Problems." In Finite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems, 157–213. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-23588-7_3.

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Freeden, Willi, and Volker Michel. "Satellite Problems." In Multiscale Potential Theory, 333–99. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-2048-0_5.

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Chung, Eric, Yalchin Efendiev, and Thomas Y. Hou. "GMsFEM for nonlinear problems." In Multiscale Model Reduction, 397–411. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-20409-8_14.

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Freeden, Willi, and Volker Michel. "Boundary-Value Problems of Elasticity." In Multiscale Potential Theory, 267–329. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-2048-0_4.

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Freeden, Willi, and Volker Michel. "Boundary-Value Problems of Potential Theory." In Multiscale Potential Theory, 71–266. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-2048-0_3.

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Cristiani, Emiliano, Benedetto Piccoli, and Andrea Tosin. "Problems and Simulations." In Multiscale Modeling of Pedestrian Dynamics, 29–52. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06620-2_2.

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Michel, Volker. "Tomography: Problems and Multiscale Solutions." In Handbook of Geomathematics, 949–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-01546-5_32.

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Michel, Volker. "Tomography: Problems and Multiscale Solutions." In Handbook of Geomathematics, 2087–119. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-642-54551-1_32.

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Parés, C. "Minisymposium “Multiscale Problems in Materials”." In Progress in Industrial Mathematics at ECMI 2006, 340. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-71992-2_48.

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Carpio, A. "Minisymposium “Multiscale Problems in Materials”." In Progress in Industrial Mathematics at ECMI 2006, 366–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-71992-2_54.

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Conference papers on the topic "Multiscale problems"

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Graglia, Roberto D., Andrew F. Peterson, Paolo Petrini, and Ladislau Matekovits. "Hierarchical functions for multiscale problems." In 2016 IEEE International Conference on Computational Electromagnetics (ICCEM). IEEE, 2016. http://dx.doi.org/10.1109/compem.2016.7588623.

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Brož, P. "Multiscale interpretation of contact problems." In CONTACT AND SURFACE 2011. Southampton, UK: WIT Press, 2011. http://dx.doi.org/10.2495/secm110101.

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Brick, Yaniv, Jackson Massey, Kai Yang, and Ali E. Yilmaz. "All multiscale problems are hard, some are harder: A nomenclature for classifying multiscale electromagnetic problems." In 2016 USNC-URSI Radio Science Meeting (Joint with AP-S Symposium). IEEE, 2016. http://dx.doi.org/10.1109/usnc-ursi.2016.7588504.

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Kim, Jong-Han, Matthew West, Sanjay Lall, Eelco Scholte, and Andrzej Banaszuk. "Stochastic multiscale approaches to consensus problems." In 2008 47th IEEE Conference on Decision and Control. IEEE, 2008. http://dx.doi.org/10.1109/cdc.2008.4739252.

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Geiser, Jurgen. "Iterative Splitting Methods for Multiscale Problems." In 2013 12th International Symposium on Distributed Computing and Applications to Business, Engineering & Science (DCABES). IEEE, 2013. http://dx.doi.org/10.1109/dcabes.2013.7.

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Frese, Thomas, Charles A. Bouman, and Ken D. Sauer. "Multiscale models for Bayesian inverse problems." In SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, edited by Michael A. Unser, Akram Aldroubi, and Andrew F. Laine. SPIE, 1999. http://dx.doi.org/10.1117/12.366832.

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Tao, Wen-Quan, and Ya-Ling He. "Multiscale Simulations of Heat Transfer and Fluid Flow Problems." In 2010 14th International Heat Transfer Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/ihtc14-23408.

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Abstract:
Multiscale simulation is a rapidly evolving area of research that will have a great impact on computational mathematics and numerical modeling in engineering. In this keynote lecture following parts are included. First, what is multiscale problem. In the thermal and fluid science multiscale problems may be classified into two categories: multiscale process and multiscale system. By multiscale process we mean that the overall behavior is governed by processes occur at different length scales. By multiscale system we refer to a system that is characterized by a large variation in length scales. The cooling of an electronic system is such a typical multiscale system. Existing numerical methods for three geometric scales (macro, meso and micro) are briefly mentioned. In the second part the necessity of multiscale simulation is discussed. Examples are provided for multiscale process and multiscale system. In this lecture focus is put on the simulation of multiscale process. In the third section numerical approaches developed for the simulation of multiscale processes are presented. There are two types of simulation approaches. One is the usage of a general governing equation and solving the entire flow field involving a variation of several orders in characteristic geometric scale. The other is the so-called “solving regionally and coupling at the interfaces”. In this approach the processes at different length level is simulated by different numerical methods and then information is exchanged at the interfaces between different regions. The exchange of information should be conducted in a way that is physically meaningful, mathematically stable, and computationally efficient. The key point is the establishment of the reconstruction operator, which transforms the data of few variables of macroscopic computation to large amount of variables of microscale or mesoscale simulation. For different coupling cases the existing methods for such operators are briefly reviewed. In the fourth part, four numerical examples of multiscale simulation are presented: liquid flow in nanochannels with roughness by using MDS and FVM, flow and heat transfer in a micro nozzle by using DSMC in fluid and FVM in solid, flow past a cylinder and natural convection heat transfer in a square cavity by using coupled FVM and LBM. Finally, it is pointed out that we have a long way to go in order to have a successful full multiscale simulation for the complicated engineering problems as transport process in PEMFC and refrigerant condensation process on a enhanced surface. Further researches are highly required to establish robust and quick-convergent numerical solution approaches. Some further research needs are proposed.
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He, Xinbo, Bing Wei, and Kaihang Fan. "An Effective FDTD Method for Multiscale Problems." In 2019 International Applied Computational Electromagnetics Society Symposium - China (ACES). IEEE, 2019. http://dx.doi.org/10.23919/aces48530.2019.9060619.

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Erdogan, Fazil, Glaucio H. Paulino, Marek-Jerzy Pindera, Robert H. Dodds, Fernando A. Rochinha, Eshan Dave, and Linfeng Chen. "Mixed Boundary Value Problems in Mechanics of Materials “Some Reflections on Forty Years of Solving Mixed Boundary Value Problems in Inhomogeneous Elasticity”." In MULTISCALE AND FUNCTIONALLY GRADED MATERIALS 2006. AIP, 2008. http://dx.doi.org/10.1063/1.2896880.

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Graglia, Roberto D., Paolo Petrini, Ladislau Matekovits, and Andrew F. Peterson. "Singular and hierarchical vector functions for multiscale problems." In 2016 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting. IEEE, 2016. http://dx.doi.org/10.1109/aps.2016.7695828.

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Reports on the topic "Multiscale problems"

1

Berlyand, Leonid. Finite Dimensional Approximations for Continuum Multiscale Problems. Office of Scientific and Technical Information (OSTI), January 2017. http://dx.doi.org/10.2172/1340478.

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Miller, Eric, and Alan Willsky. A Multiscale Approach to Solving One Dimensional Inverse Problems. Fort Belvoir, VA: Defense Technical Information Center, January 1992. http://dx.doi.org/10.21236/ada459602.

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Efendiev, Yalchin, Maria Vasilyeva, and Bani Mallick. Scalable Multilevel Uncertainty Quantification Concepts for Extreme-Scale Multiscale Problems. Office of Scientific and Technical Information (OSTI), December 2018. http://dx.doi.org/10.2172/1485812.

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Miller, Eric L., and Alan S. Willsky. A Multiscale, Statistically-Based Inversion Scheme for Linearized Inverse Scattering Problems. Fort Belvoir, VA: Defense Technical Information Center, September 1994. http://dx.doi.org/10.21236/ada458526.

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Oden, J. T. Modeling and Computational Analysis of Multiscale Phenomena in Fluid-Structure Interaction Problems. Fort Belvoir, VA: Defense Technical Information Center, March 1992. http://dx.doi.org/10.21236/ada248723.

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Donald Estep, Michael Holst, and Simon Tavener. A Posteriori Analysis of Adaptive Multiscale Operator Decomposition Methods for Multiphysics Problems. Office of Scientific and Technical Information (OSTI), February 2010. http://dx.doi.org/10.2172/971515.

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Doyle III, Francis J. Multiscale Problems in Circadian Systems Biology: From Gene to Cell to Performance. Fort Belvoir, VA: Defense Technical Information Center, March 2012. http://dx.doi.org/10.21236/ada570943.

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Shu, Chi-Wang. High Order Accurate Algorithms for Shocks, Rapidly Changing Solutions and Multiscale Problems. Fort Belvoir, VA: Defense Technical Information Center, January 2013. http://dx.doi.org/10.21236/ada583317.

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Shu, Chi-Wang. High Order Accurate Algorithms for Shocks, Rapidly Changing Solutions and Multiscale Problems. Fort Belvoir, VA: Defense Technical Information Center, November 2014. http://dx.doi.org/10.21236/ada617663.

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Miller, Eric L., and Alan S. Willsky. A Multiscale Approach to Sensor Fusion and the Solution of Linear Inverse Problems. Fort Belvoir, VA: Defense Technical Information Center, December 1993. http://dx.doi.org/10.21236/ada458527.

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