Related papers: Adaptive BEM with inexact PCG solver yields almost…
We consider a finite element method for elliptic equation with heterogeneous and possibly high-contrast coefficients based on primal hybrid formulation. A space decomposition as in FETI and BDCC allows a sequential computations of the…
Multigrid methods are asymptotically optimal algorithms ideal for large-scale simulations. But, they require making numerous algorithmic choices that significantly influence their efficiency. Unlike recent approaches that learn optimal…
The ultimate goal of any numerical scheme for partial differential equations (PDEs) is to compute an approximation of user-prescribed accuracy at quasi-minimal computational time. To this end, algorithmically, the standard adaptive finite…
Many problems in geophysical and atmospheric modelling require the fast solution of elliptic partial differential equations (PDEs) in "flat" three dimensional geometries. In particular, an anisotropic elliptic PDE for the pressure…
In this paper we are concerned with restricted additive Schwarz with local impedance transformation conditions for a family of Helmholtz problems in two dimensions. These problems are discretized by the finite element method with conforming…
We prove convergence with optimal algebraic rates for an adaptive finite element method for nonlinear equations with strongly monotone operator. Unlike prior works, our analysis also includes the iterative and inexact solution of the…
We propose a new adaptive algorithm for the approximation of the Landau-Lifshitz-Gilbert equation via a higher-order tangent plane scheme. We show that the adaptive approximation satisfies an energy inequality and demonstrate numerically,…
We present a fully iterative adaptive algorithm for the numerical minimization of strongly convex energy functionals in Hilbert spaces. The proposed approach, which we first present in abstract form, generates a hierarchical sequence of…
We present numerical experiments for geophysics electromagnetic (EM) modeling based upon high-order edge elements and supervised $h+p$ refinement approaches on massively parallel computers. Our high-order $h+p$ refinement strategy is based…
We develop a boundary integral equation-based numerical method to solve for the electrostatic potential in two dimensions, inside a medium with piecewise constant conductivity, where the boundary condition is given by the complete electrode…
In recent years there have been tremendous advances in the theoretical understanding of boundary integral equations for Maxwell problems. In particular, stable dual pairing of discretisation spaces have been developed that allow robust…
The polar coordinate transformation (PCT) method has been extensively used to treat various singular integrals in the boundary element method (BEM). However, the resultant integrands of the PCT tend to become nearly singular when (1) the…
Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment.…
Domain decomposition methods are among the most efficient for solving sparse linear systems of equations. Their effectiveness relies on a judiciously chosen coarse space. Originally introduced and theoretically proved to be efficient for…
In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…
This work is concerned with the numerical solution of large-scale symmetric positive definite matrix equations of the form $A_1XB_1^\top + A_2XB_2^\top + \dots + A_\ell X B_\ell^\top = F$, as they arise from discretized partial differential…
In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approximation spaces computed by solving eigenvalue problems on…
We propose a path cover adaptive algebraic multigrid (PC-$\alpha$AMG) method for solving linear systems of weighted graph Laplacians and can also be applied to discretized second order elliptic partial differential equations. The…
We investigate the application of the additive overlapping Schwarz domain decomposition method as a preconditioner for the large sparse linear systems arising in graph-based nonlinear least-squares problems, specifically the pose-graph…
We develop numerical methods for elliptic systems governed by partial segregation constraints, in which three nonnegative components are required to have a vanishing pointwise product throughout the domain. This constraint enforces that at…