In this work we present son-le numerical methods for solving evolutive convection-diffusion problems. In order to obtain a physically admissible solution we search for monotone and accurate methods that are also non-l...
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ISBN:
(数字)9783642196652
ISBN:
(纸本)9783642196645
In this work we present son-le numerical methods for solving evolutive convection-diffusion problems. In order to obtain a physically admissible solution we search for monotone and accurate methods that are also non-linear due to the Godunov's theorem. We will center in Fluctuation Splitting methods, [8], in particular in PSI scheme, and characteristic type methods, where a new Lagrangian method is proposed. Finally, a numerical test is presented to assess the performance of the numerical methods described in the present work.
The Jacobi-Davidson (JD) algorithm recently has gained popularity for finding a few selected interior eigenvalues of large sparse polynomial eigenvalue problems, which commonly appear in many computationalscience and...
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ISBN:
(纸本)9783642113031
The Jacobi-Davidson (JD) algorithm recently has gained popularity for finding a few selected interior eigenvalues of large sparse polynomial eigenvalue problems, which commonly appear in many computationalscience and engineering PDE based applications. As other inner outer algorithms like Newton type method, the bottleneck of the JD algorithm is to solve approximately the inner correction equation. In the previous work, [Hwang, Wei, Huang, and Wang, A Parallel Additive Schwarz Preconditioned Jacobi-Davidson (ASPJD) Algorithm for Polynomial Eigenvalue Problems in Quantum Dot (QD) Simulation, Journal of computational Physics (2010)], the authors proposed a parallel restricted additive Schwarz preconditioner in conjunction with a parallel Krylov subspace method to accelerate the convergence of the JD algorithm. Based on the previous computational experiences on the algorithmic parameter tuning for the ASPJD algorithm, we further investigate the parallel performance of a PETSc based ASPJD eigensolver on the Blue Gene/P, and a QD quintic eigenvalue problem is used as an example to demonstrate its scalability by showing the excellent strong scaling up to 2,048 cores.
Schwarz domain decomposition methods can be analyzed both at the continuous and discrete level. For consistent discretizations, one would naturally expect that the discretized method performs as predicted by the conti...
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ISBN:
(纸本)9783642113031
Schwarz domain decomposition methods can be analyzed both at the continuous and discrete level. For consistent discretizations, one would naturally expect that the discretized method performs as predicted by the continuous analysis. We show in this short note for two model problems that this is not always the case, and that the discretization can both increase and decrease the convergence speed predicted by the continuous analysis.
In this paper we study the finite element approximation for boundary control problems governed by semilinear elliptic equations. Optimal control problems are very important model in science and engineering numerical s...
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Poincare type inequalities play a central role in the analysis of domain decomposition and multigrid methods for second-order elliptic problems. However, when the coefficient varies within a subdomain or within a coar...
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ISBN:
(纸本)9783642113031
Poincare type inequalities play a central role in the analysis of domain decomposition and multigrid methods for second-order elliptic problems. However, when the coefficient varies within a subdomain or within a coarse grid element, then standard condition number bounds for these methods may be overly pessimistic. In this short note we present new weighted Poincare type inequalities for a class of piecewise constant coefficients that lead to sharper bounds independent of any possible large contrasts in the coefficients.
It is well accepted that the efficient solution of complex partial differential equations (PDEs) often requires methods which are adaptive in both space and time. In this paper we are interested in a class of spatiall...
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In this paper, we develop and analyze an efficient multigrid method to solve the finite element systems from elliptic obstacle problems on two dimensional adaptive meshes. Adaptive finite element methods (AFEMs) based...
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The objective of this paper is to explain the principles of the design of a coarse space in a simplified way and by pictures. The focus is on ideas rather than on a more historically complete presentation. That can be...
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