3 research outputs found
A parallel solver for a preconditioned space-time boundary element method for the heat equation
We describe a parallel solver for the discretized weakly singular space-time
boundary integral equation of the spatially two-dimensional heat equation. The
global space-time nature of the system matrices leads to improved parallel
scalability in distributed memory systems in contrast to time-stepping methods
where the parallelization is usually limited to spatial dimensions. We present
a parallelization technique which is based on a decomposition of the input mesh
into submeshes and a distribution of the corresponding blocks of the system
matrices among processors. To ensure load balancing, the distribution is based
on a cylic decomposition of complete graphs. In addition, the solution of the
global linear system requires the use of an efficient preconditioner. We
present a robust preconditioning strategy which is based on boundary integral
operators of opposite order, and extend the introduced parallel solver to the
preconditioned system.Comment: Submitted for publication in the proceedings of the 25th
International Conference on Domain Decomposition Method
New preconditioners for Laplace and Helmholtz integral equations on open curves: Analytical framework and Numerical results
The Helmholtz wave scattering problem by screens in 2D can be recast into
first-kind integral equations which lead to ill-conditioned linear systems
after discretization. We introduce two new preconditioners, in the form of
square-roots of local operators respectively for the corresponding problems
with Dirichlet and Neumann conditions on the arc. They generalize the so-called
"analytical" preconditioners available for Lipschitz scatterers. We introduce a
functional setting adapted to the singularity of the problem and enabling the
analysis of those preconditioners. The efficiency of the method is demonstrated
on several numerical examples
Optimal additive Schwarz preconditioning for adaptive 2D IGA boundary element methods
We define and analyze (local) multilevel diagonal preconditioners for
isogeometric boundary elements on locally refined meshes in two dimensions.
Hypersingular and weakly-singular integral equations are considered. We prove
that the condition number of the preconditioned systems of linear equations is
independent of the mesh-size and the refinement level. Therefore, the
computational complexity, when using appropriate iterative solvers, is optimal.
Our analysis is carried out for closed and open boundaries and numerical
examples confirm our theoretical results.Comment: accepted in Computer Methods in Applied Mechanics and Engineerin