We consider a stationary Stokes interface problem. In the discretization the interface is not aligned with the triangulation. For the discretization we use the P1 extended finite element space (P1-XFEM) for the pressure and the standard conforming P2 finite element space for the velocity. Since this pair is not necessarily LBB stable, a consistent stabilization term, known from the literature, ...

We present a new preconditioner for linear systems arising from finite-elements discretizations of scalar elliptic partial differential equations (pde’s). The solver splits the collection {Ke} of element matrices into a subset E(t) of matrices that are approximable by diagonally-dominant matrices and a subset of matrices that are not approximable. The approximable Ke’s are approximated by diago...

We report on a parallel implementation of the Jacobi–Davidson algorithm to compute a few eigenvalues and corresponding eigenvectors of a large real symmetric generalized matrix eigenvalue problem Ax = λMx, Cx = 0. The eigenvalue problem stems from the design of cavities of particle accelerators. It is obtained by the finite element discretization of the time-harmonic Maxwell equation in weak fo...

For quite some times, deflation preconditioner has been proposed and used to accelerate the convergence of Krylov subspace methods. For symmetric positive definite linear systems, convergence of CG combined with deflation has been analyzed and compared with other preconditioners, e.g. with the abstract balancing preconditioner [Nabben and Vuik, SIAM J. Sci. Comput., 27 (2006), pp. 1742–1759]. I...

We study preconditioning techniques used in conjunction with the conjugate gradient method for solving multi-length-scale symmetric positive definite linear systems originating from the quantum Monte Carlo simulation of electron interaction of correlated materials. Existing preconditioning techniques are not designed to be adaptive to varying numerical properties of the multi-length-scale syste...

Parallel overlapping Schwarz preconditioners are considered and applied to the structural block in monolithic fluid-structure interaction (FSI). The two-level overlapping Schwarz method uses a coarse level based on energy minimizing functions. Linear elastic as well as nonlinear, anisotropic hyperelastic structural models are considered in an FSI problem of a pressure wave in a tube. Using our ...

For the iterative solution of saddle point problems, a nonsymmetric preconditioner is studied which, with respect to the upper-left block of the system matrix, can be seen as a variant of SSOR. An idealized situation where SSOR is taken with respect to the skew-symmetric part plus the diagonal part of the upper-left block is analyzed in detail. Since action of the preconditioner involves soluti...

This paper presents an efficient preconditioner for the Lippmann-Schwinger equation that combines the ideas of the sparsifying and the sweeping preconditioners. Following first the idea of the sparsifying preconditioner, this new preconditioner starts by transforming the dense linear system of the Lippmann-Schwinger equation into a nearly sparse system. The key novelty is a newly designed perfe...