The boundary element method has become a popular tool for the solution of Maxwell’s equations in electromagnetism. From a linear algebra point of view, this leads to the solution of large dense complex linear systems where the unknowns are associated with the edges of the mesh defined on the surface of the illuminated object. In this paper, we address the iterative solution of these linear syst...

Block lower triangular and block upper triangular matrices are popular preconditioners for nonsymmetric saddle point matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned systems are related. Nonsingular saddle point matrices of the form

In this paper, we study an efficient tridiagonal preconditioner, based on numerical differentiation, applied to the matrix-free truncated Newton method for unconstrained optimization. It is proved that this preconditioner is positive definite for many practical problems. The efficiency of the resulting matrix-free truncated Newton method is demonstrated by results of extensive numerical experim...

In this paper we analyse in detail the spectral properties of the block-triangular preconditioner for the Bidomain system in non-symmetric form, introduced in [8]. We provide an explicit formula to optimize the preconditioner performance, and we illustrate our findings with some numerical test in three dimensions.

In this paper it is shown that for highly nonuniformly refined triangulations the condition number of the BPX preconditioner for elliptic finite element problems grows at most linearly in the depth of refinement. This is achieved by viewing the computational available version of the BPX preconditioner as an abstract additive Schwarz method with exact solvers. AMS CLASSIFICATION: 65F10, 65F35, 6...

This paper is concerned with parallel computation in solving the convection-diffusion equation and the incompressible Navier-Stokes equation via Newton-Schwarz method, a nonlinear domain decomposition (DD) method. Various preconditioners are investigated here. An interface problem is tackled as a preconditioner for nonlinear block Jacobi DD approach, with an optional fine level interface proble...

We present a new preconditioner for linear systems arising from finite-element discretizations of scalar elliptic partial differential equations (PDE’s). The solver splits the collection {Ke} of element matrices into a subset 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 diagonally ...

We have defined and analyzed a semi-Toeplitz preconditioner for timedependent and steady-state convection-diffusion problems. Analytic expressions for the eigenvalues of the preconditioned systems are obtained. An asymptotic analysis shows that the eigenvalue spectrum of the timedependent problem is reduced to two eigenvalues when the number of grid points go to infinity. The numerical experime...

Abstract. Recently a new algorithm for model reduction of second order linear dynamical systems with proportional damping, the Adaptive Iterative Rational Global Arnoldi (AIRGA) algorithm [8], has been proposed. The main computational cost of the AIRGA algorithm is in solving a sequence of linear systems. These linear systems do change only slightly from one iteration step to the next. Here we ...

We study the Stokes equation with high-contrast viscosity coefficient and this regime corresponds to a small Reynolds number regime because viscosity is inversely proportional to the Reynolds number. Numerical solution to the Stokes flow problems especially with high-contrast variations in viscosity is critically needed in the computational geodynamics community. One of the main applications of...