Displaying similar documents to “Some practical aspects of parallel adaptive BDDC method”

On multipoint constraints in FETI methods

Pavla Hrušková, Zdeněk Dostál, Oldřich Vlach, Petr Vodstrčil (2025)

Applications of Mathematics

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FETI (finite element tearing and interconnecting) based domain decomposition methods are well-established massively parallel methods for solving huge linear systems arising from discretizing partial differential equations. The first steps of FETI decompose the domain into nonoverlapping subdomains, discretize the subdomains using matching grids, and interconnect the adjacent variables by multipoint constraints. However, the multipoint constraints enforcing identification of the corners'...

Object oriented design philosophy for scientific computing

Philippe R.B. Devloo, Gustavo C. Longhin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This contribution gives an overview of current research in applying object oriented programming to scientific computing at the computational mechanics laboratory (LABMEC) at the school of civil engineering – UNICAMP. The main goal of applying object oriented programming to scientific computing is to implement increasingly complex algorithms in a structured manner and to hide the complexity behind a simple user interface. The following areas are current topics of research and documented...

An asynchronous three-field domain decomposition method for first-order evolution problems

Krupička, Lukáš, Beneš, Michal

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We present an asynchronous multi-domain time integration algorithm with a dual domain decomposition method for the initial boundary-value problems for a parabolic equation. For efficient parallel computing, we apply the three-field domain decomposition method with local Lagrange multipliers to ensure the continuity of the primary unknowns at the interface between subdomains. The implicit method for time discretization and the multi-domain spatial decomposition enable us to use different...

A multilevel preconditioner for the mortar method for nonconforming finite element

Talal Rahman, Xuejun Xu (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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A multilevel preconditioner based on the abstract framework of the auxiliary space method, is developed for the mortar method for the nonconforming finite element or the lowest order Crouzeix-Raviart finite element on nonmatching grids. It is shown that the proposed preconditioner is quasi-optimal in the sense that the condition number of the preconditioned system is independent of the mesh size, and depends only quadratically on the number of refinement levels. Some...

FER/SubDomain : an integrated environment for finite element analysis using object-oriented approach

Zhi-Qiang Feng, Jean-Michel Cros (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Development of user-friendly and flexible scientific programs is a key to their usage, extension and maintenance. This paper presents an OOP (Object-Oriented Programming) approach for design of finite element analysis programs. General organization of the developed software system, called FER/SubDomain, is given which includes the solver and the pre/post processors with a friendly GUI (Graphical User Interfaces). A case study with graphical representations illustrates some functionalities...

Algebraic domain decomposition solver for linear elasticity

Aleš Janka (1999)

Applications of Mathematics

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We generalize the overlapping Schwarz domain decomposition method to problems of linear elasticity. The convergence rate independent of the mesh size, coarse-space size, Korn’s constant and essential boundary conditions is proved here. Abstract convergence bounds developed here can be used for an analysis of the method applied to singular perturbations of other elliptic problems.