38 research outputs found
Numerical comparison of different choices of interface weights in the BDDC method
summary:Balancing Domain Decomposition by Constraints (BDDC) belongs to the class of primal substructuring Domain Decomposition (DD) methods. DD methods are iterative methods successfully used in engineering to parallelize solution of large linear systems arising from discretization of second order elliptic problems. Substructuring DD methods represent an important class of DD methods. Their main idea is to divide the underlying domain into nonoverlapping subdomains and solve many relatively small, local problems on subdomains instead of one large problem on the whole domain. In primal methods, it has to be specified how to distribute interface residuals among subdomains and how to obtain global, interface values of solution from local values on adjacent subdomains. Usually a weighted average is used with some simple choice of weights. In our paper we present numerical comparison of three different choices of interface weights on test problem of 2D Poisson equation, with and without jumps in coefficients
An application of the BDDC method to the Navier-Stokes equations in 3-D cavity
summary:We deal with numerical simulation of incompressible flow governed by the Navier-Stokes equations. The problem is discretised using the finite element method, and the arising system of nonlinear equations is solved by Picard iteration. We explore the applicability of the Balancing Domain Decomposition by Constraints (BDDC) method to nonsymmetric problems arising from such linearisation. One step of BDDC is applied as the preconditioner for the stabilized variant of the biconjugate gradient (BiCGstab) method. We present results for a 3-D cavity problem computed on 32 cores of a parallel supercomputer
A New Mechanism for Maintaining Diversity of Pareto Archive in Multiobjective Optimization
The article introduces a new mechanism for selecting individuals to a Pareto
archive. It was combined with a micro-genetic algorithm and tested on several
problems. The ability of this approach to produce individuals uniformly
distributed along the Pareto set without negative impact on convergence is
demonstrated on presented results. The new concept was confronted with NSGA-II,
SPEA2, and IBEA algorithms from the PISA package. Another studied effect is the
size of population versus number of generations for small populations.Comment: 51 pages, 28 figure
Adaptive BDDC in Three Dimensions
The adaptive BDDC method is extended to the selection of face constraints in
three dimensions. A new implementation of the BDDC method is presented based on
a global formulation without an explicit coarse problem, with massive
parallelism provided by a multifrontal solver. Constraints are implemented by a
projection and sparsity of the projected operator is preserved by a generalized
change of variables. The effectiveness of the method is illustrated on several
engineering problems.Comment: 28 pages, 9 figures, 9 table
BDDC by a frontal solver and the stress computation in a hip joint replacement
A parallel implementation of the BDDC method using the frontal solver is
employed to solve systems of linear equations from finite element analysis, and
incorporated into a standard finite element system for engineering analysis by
linear elasticity. Results of computation of stress in a hip replacement are
presented. The part is made of titanium and loaded by the weight of human body.
The performance of BDDC with added constraints by averages and with added
corners is compared.Comment: Expanded, 22 pages, 8 figure
Application of the parallel BDDC preconditioner to the Stokes flow
A parallel implementation of the Balancing Domain Decomposition by
Constraints (BDDC) method is described. It is based on formulation of BDDC with
global matrices without explicit coarse problem. The implementation is based on
the MUMPS parallel solver for computing the approximate inverse used for
preconditioning. It is successfully applied to several problems of Stokes flow
discretized by Taylor-Hood finite elements and BDDC is shown to be a promising
method also for this class of problems.Comment: 27 pages, 5 figures, 7 table
A parallel finite element solver for unsteady incompressible Navier-Stokes equations
A parallel solver for unsteady incompressible Navier-Stokes equations is presented. It is based on the finite element method combined with the pressure-correction approach. Semi-implicit treatment of the convective term is considered, leading to five systems of linear algebraic equations to be solved in each time step. Krylov subspace iterative methods are employed for the solution of these systems with a particular emphasis on efficient parallel preconditioners. A simulation of a benchmark problem of incompressible viscous flow around a sphere at Reynolds number 300 is presented and compared with literature