Relevant bibliographies by topics / Schwarz methods

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

Academic literature on the topic 'Schwarz methods'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Schwarz methods"

1

Gander, Martin J. "Optimized Schwarz Methods." SIAM Journal on Numerical Analysis 44, no. 2 (January 2006): 699–731. http://dx.doi.org/10.1137/s0036142903425409.

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Zhang, Xuejun. "Multilevel Schwarz methods." Numerische Mathematik 63, no. 1 (December 1992): 521–39. http://dx.doi.org/10.1007/bf01385873.

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Gander, Martin J., and Tommaso Vanzan. "Multilevel Optimized Schwarz Methods." SIAM Journal on Scientific Computing 42, no. 5 (January 2020): A3180—A3209. http://dx.doi.org/10.1137/19m1259389.

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da Veiga, L. Beira͂o, D. Cho, L. F. Pavarino, and S. Scacchi. "Overlapping Schwarz Methods for Isogeometric Analysis." SIAM Journal on Numerical Analysis 50, no. 3 (January 2012): 1394–416. http://dx.doi.org/10.1137/110833476.

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Cai, Xiao-Chuan. "Multiplicative Schwarz Methods for Parabolic Problems." SIAM Journal on Scientific Computing 15, no. 3 (May 1994): 587–603. http://dx.doi.org/10.1137/0915039.

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Rui, Hongxing. "Multiplicative Schwarz methods for parabolic problems." Applied Mathematics and Computation 136, no. 2-3 (March 2003): 593–610. http://dx.doi.org/10.1016/s0096-3003(02)00085-1.

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Canuto, C., and D. Funaro. "The Schwarz Algorithm for Spectral Methods." SIAM Journal on Numerical Analysis 25, no. 1 (February 1988): 24–40. http://dx.doi.org/10.1137/0725003.

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Dolean, V., M. J. Gander, and L. Gerardo-Giorda. "Optimized Schwarz Methods for Maxwell's Equations." SIAM Journal on Scientific Computing 31, no. 3 (January 2009): 2193–213. http://dx.doi.org/10.1137/080728536.

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Griebel, Michael, and Peter Oswald. "Schwarz Iterative Methods: Infinite Space Splittings." Constructive Approximation 44, no. 1 (November 17, 2015): 121–39. http://dx.doi.org/10.1007/s00365-015-9318-y.

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Yang, Jianhua, and Danping Yang. "Additive Schwarz methods for parabolic problems." Applied Mathematics and Computation 163, no. 1 (April 2005): 17–28. http://dx.doi.org/10.1016/j.amc.2004.03.025.

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Dissertations / Theses on the topic "Schwarz methods"

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Dubois, Olivier. "Optimized Schwarz methods for the advection-diffusion equation." Thesis, McGill University, 2003. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=19701.

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The optimized Schwarz methods were recently introduced to enhance the convergence of the classical Schwarz iteration, by replacing the Dirichlet transmission conditions with different conditions obtained through an optimization of the convergence rate. This is formulated as a min-max problem. These new methods are well-studied for elliptic second order symmetric equations. The purpose of this work is to compute optimized Robin transmission conditions for the advection-diffusion equation in two dimensions, by finding the solution of the min-max problem. The asymptotic expansion, for small mesh size h, of the resulting convergence rate is found: it shows a weak dependence on h, if the overlap is 0(h) or no overlap is used. Numerical experiments illustrate the improved convergence of these optimized methods compared to other Schwarz methods, and also justify the continuous Fourier analysis performed on a simple model problem only. The theoretical asymptotic performance is also verified numerically.
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Tang, Wei-pai. "Schwarz splitting and template operators." Stanford, CA : Dept. of Computer Science, Stanford University, 1987. http://doi.library.cmu.edu/10.1184/OCLC/19643650.

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Thesis (Ph. D.)--Stanford University, 1987.
"June 1987." "Also numbered Classic-87-03"--Cover. "This research was supported by NASA Ames Consortium Agreement NASA NCA2-150 and Office of Naval Research Contracts N00014-86-K-0565, N00014-82-K-0335, N00014-75-C-1132"--P. vi. Includes bibliographical references (p. 125-129).
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Karangelis, Anastasios. "Analysis and massively parallel implementation of the 2-Lagrange multiplier methods and optimized Schwarz methods." Thesis, Heriot-Watt University, 2016. http://hdl.handle.net/10399/3102.

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Garay, Jose. "Asynchronous Optimized Schwarz Methods for Partial Differential Equations in Rectangular Domains." Diss., Temple University Libraries, 2018. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/510451.

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Mathematics
Ph.D.
Asynchronous iterative algorithms are parallel iterative algorithms in which communications and iterations are not synchronized among processors. Thus, as soon as a processing unit finishes its own calculations, it starts the next cycle with the latest data received during a previous cycle, without waiting for any other processing unit to complete its own calculation. These algorithms increase the number of updates in some processors (as compared to the synchronous case) but suppress most idle times. This usually results in a reduction of the (execution) time to achieve convergence. Optimized Schwarz methods (OSM) are domain decomposition methods in which the transmission conditions between subdomains contain operators of the form \linebreak $\partial/\partial \nu +\Lambda$, where $\partial/\partial \nu$ is the outward normal derivative and $\Lambda$ is an optimized local approximation of the global Steklov-Poincar\'e operator. There is more than one family of transmission conditions that can be used for a given partial differential equation (e.g., the $OO0$ and $OO2$ families), each of these families containing a particular approximation of the Steklov-Poincar\'e operator. These transmission conditions have some parameters that are tuned to obtain a fast convergence rate. Optimized Schwarz methods are fast in terms of iteration count and can be implemented asynchronously. In this thesis we analyze the convergence behavior of the synchronous and asynchronous implementation of OSM applied to solve partial differential equations with a shifted Laplacian operator in bounded rectangular domains. We analyze two cases. In the first case we have a shift that can be either positive, negative or zero, a one-way domain decomposition and transmission conditions of the $OO2$ family. In the second case we have Poisson's equation, a domain decomposition with cross-points and $OO0$ transmission conditions. In both cases we reformulate the equations defining the problem into a fixed point iteration that is suitable for our analysis, then derive convergence proofs and analyze how the convergence rate varies with the number of subdomains, the amount of overlap, and the values of the parameters introduced in the transmission conditions. Additionally, we find the optimal values of the parameters and present some numerical experiments for the second case illustrating our theoretical results. To our knowledge this is the first time that a convergence analysis of optimized Schwarz is presented for bounded subdomains with multiple subdomains and arbitrary overlap. The analysis presented in this thesis also applies to problems with more general domains which can be decomposed as a union of rectangles.
Temple University--Theses
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Fritz, Manuel [Verfasser], and Holger [Akademischer Betreuer] Schwarz. "Methods for enhanced exploratory clustering analyses / Manuel Fritz ; Betreuer: Holger Schwarz." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2021. http://d-nb.info/1237270723/34.

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Schwarz, Jolanda M. [Verfasser]. "Advanced Image Reconstruction Methods for Ultra-High Field MRI / Jolanda M. Schwarz." Bonn : Universitäts- und Landesbibliothek Bonn, 2020. http://d-nb.info/1218474947/34.

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Shakir, Noman [Verfasser], and Guido [Akademischer Betreuer] Kanschat. "Multilevel Schwarz Methods for Incompressible Flow Problems / Noman Shakir ; Betreuer: Guido Kanschat." Heidelberg : Universitätsbibliothek Heidelberg, 2017. http://d-nb.info/1180986784/34.

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Ovtchinnikov, Serguei. "Parallel implicit fully coupled Newton-Krylov-Schwarz methods for numerical simulations of magnetohydrodynamics." Diss., Connect to online resource, 2006. 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:3239463.

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Du, Xiuhong. "Additive Schwarz Preconditioned GMRES, Inexact Krylov Subspace Methods, and Applications of Inexact CG." Diss., Temple University Libraries, 2008. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/6474.

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Mathematics
Ph.D.
The GMRES method is a widely used iterative method for solving the linear systems, of the form Ax = b, especially for the solution of discretized partial differential equations. With an appropriate preconditioner, the solution of the linear system Ax = b can be achieved with less computational effort. Additive Schwarz Preconditioners have two good properties. First, they are easily parallelizable, since several smaller linear systems need to be solved: one system for each of the sub-domains, usually corresponding to the restriction of the differential operator to that subdomain. These are called local problems. Second, if a coarse problem is introduced, they are optimal in the sense that bounds on the convergence rate of the preconditioned iterative method are independent (or slowly dependent) on the finite element mesh size and the number of subproblems. We study certain cases where the same optimality can be obtained without a coarse grid correction. In another part of this thesis we consider inexact GMRES when applied to singular (or nearly singular) linear systems. This applies when instead of matrix-vector products with A, one uses A = A+E for some error matrix E which usually changes from one iteration to the next. Following a similar study by Simoncini and Szyld (2003) for nonsingular systems, we prescribe how to relax the exactness of the matrixvector product and still achieve the desired convergence. In addition, similar criteria is given to guarantee that the computed residual with the inexact method is close to the true residual. Furthermore, we give a new computable criteria to determine the inexactness of matrix-vector product using in inexact CG, and applied it onto control problems governed by parabolic partial differential equations.
Temple University--Theses
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Terkhova, Karina. "Capacitance matrix preconditioning." Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244593.

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Books on the topic "Schwarz methods"

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Zhang, Xuejun. Multilevel additive Schwarz methods. New York: Courant Institute of Mathematical Sciences, New York University, 1991.

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Stephan, Ernst P., and Thanh Tran. Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-79283-1.

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Cai, Xiao-Chuan. Newton-Krylov-Schwarz: An implicit solver for CFD. Hampton, Va: Institute for Computer Applications in Science and Engineering, 1995.

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Widlund, Olof B. Some Schwarz methods for symmetric and nonsymmetric elliptic problems. New York: Courant Institute of Mathematical Sciences, New York University, 1991.

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Dryja, Maksymilian. Additive Schwarz methods for elliptic finite element problems in three dimensions. New York: Courant Institute of Mathematical Sciences, New York University, 1991.

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Harry E. Schwarz and the development of water resources and environmental planning: Planning methods in an era of challenge and change. Alexandria, VA: IWR Press, 2010.

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Pavarino, Luca F. An aditive Schwarz method for the p-version finite element method. New York: Courant Institute of Mathematical Sciences, New York University, 1991.

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Pavarino, Luca F. An aditive Schwarz method for the p-version finite element method. New York: Courant Institute of Mathematical Sciences, New York University, 1991.

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Tsang, Kalvin C. H. Parallel implicit Newton-Krylov-Schwarz method for predicting compressible turbomachinery flows. [Downsview, Ont.]: University of Toronto, Institute for Aerospace Studies, 2003.

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Infinitesimal methods of mathematical analysis. Chichester, West Sussex: Horwood, 2004.

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Book chapters on the topic "Schwarz methods"

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Nataf, F. "Optimized Schwarz Methods." In Lecture Notes in Computational Science and Engineering, 233–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02677-5_25.

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Li, Zi Cai. "Schwarz Alternating Method." In Combined Methods for Elliptic Equations with Singularities, Interfaces and Infinities, 423–42. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4613-3338-8_16.

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Toselli, Andrea, and Olof B. Widlund. "Abstract Theory of Schwarz Methods." In Springer Series in Computational Mathematics, 35–53. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/3-540-26662-3_2.

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Gander, Martin J., Yao-Lin Jiang, and Rong-Jian Li. "Parareal Schwarz Waveform Relaxation Methods." In Lecture Notes in Computational Science and Engineering, 451–58. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-35275-1_53.

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Brenner, Susanne C. "An Additive Schwarz Analysis for Multiplicative Schwarz Methods: General Case." In Lecture Notes in Computational Science and Engineering, 17–30. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-93873-8_2.

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Cai, X. C., W. D. Gropp, D. E. Keyes, and M. D. Tidriri. "Newton-Krylov-Schwarz Methods in CFD." In Numerical methods for the Navier-Stokes equations, 17–30. Wiesbaden: Vieweg+Teubner Verlag, 1994. http://dx.doi.org/10.1007/978-3-663-14007-8_3.

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MacMullen, H., E. OŔiordan, and G. I. Shishkin. "Schwarz Methods for Convection-Diffusion Problems." In Lecture Notes in Computer Science, 544–51. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-45262-1_64.

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Yu, Yi, Maksymilian Dryja, and Marcus Sarkis. "Non-overlapping Spectral Additive Schwarz Methods." In Lecture Notes in Computational Science and Engineering, 375–82. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-56750-7_43.

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Stephan, Ernst P., and Thanh Tran. "Additive Schwarz Methods for the hp-Version." In Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods, 127–41. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-79283-1_6.

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Gander, Martin J., Laurence Halpern, Florence Hubert, and Stella Krell. "Optimized Overlapping DDFV Schwarz Algorithms." In Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, 365–73. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43651-3_33.

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Conference papers on the topic "Schwarz methods"

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Pospiech, Christoph. "An APL2 tool box investigating Schwarz methods." In the international conference. New York, New York, USA: ACM Press, 1992. http://dx.doi.org/10.1145/144045.144121.

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ANTONIETTI, P. F., and B. AYUSO. "MULTIPLICATIVE SCHWARZ ALGORITHMS FOR SYMMETRIC DISCONTINUOUS GALERKIN METHODS." In Selected Contributions from the 8th SIMAI Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812709394_0007.

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Wang, Guangbin, Hao Wen, and Fuping Tan. "Synchronous Multi-splitting and Schwarz Methods for Solving Linear Complementarity Problems." In 2008 International Symposium on Computer Science and Computational Technology. IEEE, 2008. http://dx.doi.org/10.1109/iscsct.2008.145.

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Houstis, E. N., J. R. Rice, and E. A. Vavalis. "A Schwarz splitting variant of cubic spline collocation methods for elliptic PDEs." In the third conference. New York, New York, USA: ACM Press, 1988. http://dx.doi.org/10.1145/63047.63133.

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Zhilyakova, Elena, Oleg Novikov, Dmitriy Pisarev, and Liliya Zolotareva. "Development of Methods For Quantitative Determination of Polyphenols in Grass Pentaphylloides Fruticosa (L.) O. Schwarz." In Proceedings of the 1st International Symposium Innovations in Life Sciences (ISILS 2019). Paris, France: Atlantis Press, 2019. http://dx.doi.org/10.2991/isils-19.2019.88.

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Li Hong Wei. "A new two-level Schwarz method." In Proceedings Fourth International Conference/Exhibition on High Performance Computing in the Asia-Pacific Region. IEEE, 2000. http://dx.doi.org/10.1109/hpc.2000.843591.

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Issa, Johnny, and Alfonso Ortega. "Numerical Computation of the Heat Transfer and Fluid Mechanics in the Laminar Wall Jet and Comparison to the Self-Similar Solutions." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-61701.

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Despite its importance as a canonical two-dimensional flow, the laminar wall jet has not been extensively studied using modern computational fluid dynamic methods. As in the laminar boundary layer, existence of analytical self-similar solutions make the problem particularly attractive for validating CFD code, yet we have found little archival work in which it has been used for this purpose. In the present study, we present a numerical investigation of the steady, laminar, and two-dimensional plane wall jet with constant properties. A finite-volume approach is used to solve the governing equations using self-similar inlet boundary conditions for the velocity and temperature profiles. The thermal solution is investigated for isothermal boundary condition at the wall. Velocity and temperature profiles are reported at various locations downstream and show an excellent agreement with the similarity solution obtained by Glauert [1] and Schwarz, et al. [2] respectively. In addition, the skin friction coefficient and the Nusselt number are investigated and compared with the analytical solutions presented by Glauert [1] and Mitachi, et al. [3] respectively, and very good agreement is observed. Despite its simplicity, it is shown that proper convergence of the numerical solutions of the wall jet to the expected analytical solutions requires care in specification of the jet inlet conditions, and the boundary conditions on the computational domain boundaries.
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Honein, Elie, Tony Honein, Michel Najjar, and Habib Rai. "On Multiple Inhomogeneities in Plane Elasticity." In ASME 2019 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/imece2019-12051.

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Abstract In this paper we present some new analytical techniques which have been recently developed to solve for problems of circular elastic inhomogeneities in anti-plane and plane elasticity. The inhomogeneities may be composed of different materials and have different radii. The matrix may be subjected to arbitrary loadings or singularities. The solution to this heterogeneous problem is sought as a transformation performed on the solution of the corresponding homogeneous problem, i.e., the problem when all the inhomogeneities are removed and the homogeneous matrix is subjected to the same loading/singularities, a procedure which has been dubbed ‘heterogenization’. In previous works, a single inhomogeneity or hole has been considered and the transformation has been shown to be purely algebraic in the antiplane case and involves differentiation of the Kolosov-Mushkelishvili complex potentials in the plane case. Universal formulas, i.e., formulas which are independent of the loading/singularities, that express the stresses at the inter-face of the inhomogeneity in terms of the stresses that would have existed at the same interface had the inhomogeneity been absent, have been be derived. The solution for a single inhomogeneity bonded to a matrix which is subjected to arbitrary loading/singularities can then in principle be used systematically in a Schwarz alternating method to obtain the solution for multiple inhomogeneities to any degree of accuracy. However alternative and innovative methods have been sought which lead to a much faster convergence and in some cases to exact expressions in terms of infinite series. The aim of this paper is to present some of the progress that has been made in this direction.
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Morishita, E. "Inverse Schwartz–Christoffel panel method." In AFM 2016. Southampton UK: WIT Press, 2016. http://dx.doi.org/10.2495/afm160151.

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Zhang, Guangsheng, Qiong Duan, Xiulan Zhu, and Feng Cao. "Application of PSO Method in Schwarz Christoffel Mapping." In 2020 International Conference on Computer Information and Big Data Applications (CIBDA). IEEE, 2020. http://dx.doi.org/10.1109/cibda50819.2020.00069.

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Reports on the topic "Schwarz methods"

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Jenkins, E. W., R. C. Berger, J. P. Hallberg, Stacy E. Howington, C. T. Kelley, Joseph H. Schmidt, Alan Stagg, and M. D. Tocci. Newton-Krylov-Schwarz Methods for Richards' Equation. Fort Belvoir, VA: Defense Technical Information Center, October 1999. http://dx.doi.org/10.21236/ada455373.

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Jenkins, E. W., R. C. Berger, J. P. Hallberg, S. E. Howington, C. T. Kelley, J. H. Schmidt, A. K. Stagg, and M. D. Tocci. A Two-Level Aggregation-Based Newton-Krylov-Schwartz Method for Hydrology. Fort Belvoir, VA: Defense Technical Information Center, January 1999. http://dx.doi.org/10.21236/ada445744.

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