The Experts below are selected from a list of 59415 Experts worldwide ranked by ideXlab platform
Olof B. Widlund - One of the best experts on this subject based on the ideXlab platform.
-
Domain Decomposition Methods in Science and Engineering XXIII - Domain Decomposition Methods in Science and Engineering XXIII
Lecture Notes in Computational Science and Engineering, 2017Co-Authors: Chang-ock Lee, David E. Keyes, Xiao-chuan Cai, Hyea Hyun Kim, Axel Klawonn, Eun-jae Park, Olof B. WidlundAbstract:This book is a collection of papers presented at the 23rd International Conference on Domain Decomposition Methods in Science and Engineering, held on Jeju Island, Korea on July 6-10, 2015. Domain Decomposition methods solve boundary value problems by splitting them into smaller boundary value problems on subDomains and iterating to coordinate the solution between adjacent subDomains. Domain Decomposition methods have considerable potential for a parallelization of the finite element methods, and serve a basis for distributed, parallel computations.
-
BDDC Deluxe Domain Decomposition
Lecture Notes in Computational Science and Engineering, 2016Co-Authors: Olof B. Widlund, Clark R. DohrmannAbstract:We will consider BDDC Domain Decomposition algorithms for finite element approximations of a variety of elliptic problems. The BDDC (Balancing Domain Decomposition by Constraints) algorithms were introduced by Dohrmann [5], following the introduction of FETI-DP by Farhat et al. [9]. These two families are closely related algorithmically and have a common theory. The design of a BDDC algorithm involves the choice of a set of primal degrees of freedom and the choice of an averaging operator, which restores the continuity of the approximate solution across the interface between the subDomains into which the Domain of the given problem has been partitioned. We will also refer to these operators as scalings.
-
Domain Decomposition Methods in Science and Engineering XXI - Domain Decomposition Methods in Science and Engineering XXI
Lecture Notes in Computational Science and Engineering, 2014Co-Authors: Jocelyne Erhel, Taoufik Sassi, Martin J. Gander, Laurence Halpern, Géraldine Pichot, Olof B. WidlundAbstract:This volume contains a selection of papers presented at the 21st international conference on Domain Decomposition methods in science and engineering held in Rennes, France, June 25-29, 2012. Domain Decomposition is an active and interdisciplinary research discipline, focusing on the development, analysis and implementation of numerical methods for massively parallel computers. Domain Decomposition methods are among the most efficient solvers for large scale applications in science and engineering. They are based on a solid theoretical foundation and shown to be scalable for many important applications. Domain Decomposition techniques can also naturally take into account multiscale phenomena. This book contains the most recent results in this important field of research, both mathematically and algorithmically and allows the reader to get an overview of this exciting branch of numerical analysis and scientific computing.
-
Domain Decomposition Methods in Science and Engineering XX - Domain Decomposition Methods in Science and Engineering XX
Lecture Notes in Computational Science and Engineering, 2013Co-Authors: Randolph E. Bank, Michael Holst, Olof B. WidlundAbstract:These are the proceedings of the 20th international conference on Domain Decomposition methods in science and engineering. Domain Decomposition methods are iterative methods for solving the often very large linearor nonlinear systems of algebraic equations that arise when various problems in continuum mechanics are discretized using finite elements. They are designed for massively parallel computers and take the memory hierarchy of such systems in mind. This is essential for approaching peak floating point performance. There is an increasingly well developed theory whichis having a direct impact on the development and improvements of these algorithms.
-
Domain Decomposition Methods in Science and Engineering XIX - Domain Decomposition methods in science and engineering XIX
Lecture Notes in Computational Science and Engineering, 2011Co-Authors: Yunqing Huang, Ralf Kornhuber, Olof B. WidlundAbstract:These are the proceedings of the 19th international conference on Domain Decomposition methods in science and engineering. Domain Decomposition methods are iterative methods for solving the often very large linear or nonlinear systems of algebraic equations that arise in various problems in mathematics, computational science, engineering and industry. They are designed for massively parallel computers and take the memory hierarchy of such systems into account. This is essential for approaching peak floating point performance. There is an increasingly well-developed theory which is having a direct impact on the development and improvement of these algorithms.
C. Le Bris - One of the best experts on this subject based on the ideXlab platform.
-
Multilevel Domain Decomposition for electronic structure calculations
Journal of Computational Physics, 2007Co-Authors: Maxime Barrault, Eric Cancès, William W. Hager, C. Le BrisAbstract:We introduce a new multilevel Domain Decomposition method (MDD) for electronic structure calculations within semi-empirical and density functional theory (DFT) frameworks. This method iterates between local fine solvers and global coarse solvers, in the spirit of Domain Decomposition methods. Using this approach, calculations have been successfully performed on several linear polymer chains containing up to 40,000 atoms and 200,000 atomic orbitals. Both the computational cost and the memory requirement scale linearly with the number of atoms. Additional speed-up can easily be obtained by parallelization. We show that this Domain Decomposition method outperforms the density matrix minimization (DMM) method for poor initial guesses. Our method provides an efficient preconditioner for DMM and other linear scaling methods, variational in nature, such as the orbital minimization (OM) procedure.
-
Multilevel Domain Decomposition for electronic structure calculations
arXiv: Computational Physics, 2005Co-Authors: Maxime Barrault, Eric Cancès, William W. Hager, C. Le BrisAbstract:We introduce a new multilevel Domain Decomposition method (MDD) for electronic structure calculations within semi-empirical and Density Functional Theory (DFT) frameworks. This method iterates between local fine solvers and global coarse solvers, in the spirit of Domain Decomposition methods.
Maxime Barrault - One of the best experts on this subject based on the ideXlab platform.
-
Multilevel Domain Decomposition for electronic structure calculations
Journal of Computational Physics, 2007Co-Authors: Maxime Barrault, Eric Cancès, William W. Hager, C. Le BrisAbstract:We introduce a new multilevel Domain Decomposition method (MDD) for electronic structure calculations within semi-empirical and density functional theory (DFT) frameworks. This method iterates between local fine solvers and global coarse solvers, in the spirit of Domain Decomposition methods. Using this approach, calculations have been successfully performed on several linear polymer chains containing up to 40,000 atoms and 200,000 atomic orbitals. Both the computational cost and the memory requirement scale linearly with the number of atoms. Additional speed-up can easily be obtained by parallelization. We show that this Domain Decomposition method outperforms the density matrix minimization (DMM) method for poor initial guesses. Our method provides an efficient preconditioner for DMM and other linear scaling methods, variational in nature, such as the orbital minimization (OM) procedure.
-
Multilevel Domain Decomposition for electronic structure calculations
arXiv: Computational Physics, 2005Co-Authors: Maxime Barrault, Eric Cancès, William W. Hager, C. Le BrisAbstract:We introduce a new multilevel Domain Decomposition method (MDD) for electronic structure calculations within semi-empirical and Density Functional Theory (DFT) frameworks. This method iterates between local fine solvers and global coarse solvers, in the spirit of Domain Decomposition methods.
Martin Vohralík - One of the best experts on this subject based on the ideXlab platform.
-
A posteriori stopping criteria for optimized Schwarz Domain Decomposition algorithms in mixed formulations
Computational Methods in Applied Mathematics, 2018Co-Authors: Sarah Ali Hassan, Caroline Japhet, Michel Kern, Martin VohralíkAbstract:This paper develops a posteriori estimates for Domain Decomposition methods with optimized Robin transmission conditions on the interface between subDomains. We choose to demonstrate the methodology for mixed formulations, with a lowest-order Raviart–Thomas–Nédélec discretization, often used for heterogeneous and anisotropic porous media diffusion problems. Our estimators allow to distinguish the spatial discretization and the Domain Decomposition error components. We propose an adaptive Domain Decomposition algorithm wherein the iterations are stopped when the Domain Decomposition error does not affect significantly the overall error. Two main goals are thus achieved. First, a guaranteed bound on the overall error is obtained at each step of the Domain Decomposition algorithm. Second, important savings in terms of the number of Domain Decomposition iterations can be realized. Numerical experiments illustrate the efficiency of our estimates and the performance of the adaptive stopping criteria.
Malgorzata Peszynska - One of the best experts on this subject based on the ideXlab platform.
-
VECPAR - Domain Decomposition for Heterojunction Problems in Semiconductors
Lecture Notes in Computer Science, 2015Co-Authors: Timothy B. Costa, David H. Foster, Malgorzata PeszynskaAbstract:We present a Domain Decomposition approach for the simulation of charge transport in heterojunction semiconductors. The problem is characterized by a large variation of primary variables across an interface region of a size much smaller than the device scale, and requires a multiscale approach in which that region is modeled as an internal boundary. The model combines drift diffusion equations on subDomains coupled by thermionic emission heterojunction model on the interface which involves a nonhomogeneous jump computed at fine scale with Density Functional Theory. Our full Domain Decomposition approach extends our previous work for the potential equation only, and we present perspectives on its HPC implementation. The model can be used, e.g., for the design of higher efficiency solar cells for which experimental results are not available. More generally, our algorithm is naturally parallelizable and is a new Domain Decomposition paradigm for problems with multiscale phenomena associated with internal interfaces and/or boundary layers.
-
Domain Decomposition for Heterojunction Problems in Semiconductors
arXiv: Computational Physics, 2014Co-Authors: Timothy B. Costa, David H. Foster, Malgorzata PeszynskaAbstract:We present a Domain Decomposition approach for the simulation of charge transport in heterojunction semiconductors. The problem is characterized by a large variation of primary variables across an interface region of a size much smaller than the device scale, and requires a multiscale approach in which that region is modeled as an internal boundary. The model combines drift diffusion equations on subDomains coupled by thermionic emission heterojunction model on the interface which involves a nonhomogeneous jump computed at fine scale with Density Functional Theory. Our full Domain Decomposition approach extends our previous work for the potential equation only, and we present perspectives on its HPC implementation. The model can be used, e.g., for the design of higher efficiency solar cells for which experimental results are not available. More generally, our algorithm is naturally parallelizable and is a new Domain Decomposition paradigm for problems with multiscale phenomena associated with internal interfaces and/or boundary layers.
