Convergence of a Multigrid Method for Elliptic Equations with Highly Oscillatory Coefficients

Multiscale Tailored Finite Point Method for Second Order Elliptic Equations with Rough or Highly Oscillatory Coefficients

We develop a multiscale tailored finite point method (MsTFPM) for second order elliptic equations with rough or highly oscillatory coefficients. The finite point method has been tailored to some particular properties of the problem, so that it can capture the multiscale solutions using coarse meshes without resolving the fine scale structure of the solution. Several numerical examples in oneand...

An octree multigrid method for quasi-static Maxwell's equations with highly discontinuous coefficients

In this paper we develop an OcTree discretization for Maxwell’s equations in the quasi-static regime. We then use this discretization in order to develop a multigrid method for Maxwell’s equations with highly discontinuous coefficients. We test our algorithms and compare it to other multilevel algorithms.

Convergence analysis of a multigrid method for convection-diffusion equations

A Multigrid Method for Nonlinear Unstructured Finite Element Elliptic Equations

This paper presents an application of the element agglomeration-based coarsening procedure (agglomeration AMGe) proposed in [10], to build the components of a multigrid method for solving nonlinear finite element elliptic equations on general unstructured meshes. The agglomeration-based AMGe offers the ability to define coarse elements and element matrices, provided access to elements and eleme...

Multigrid convergence for second order elliptic problems with smooth complex coefficients

The finite element method when applied to a second order partial differential equation in divergence form can generate operators that are neither Hermitian nor definite when the coefficient function is complex valued. For such problems, under a uniqueness assumption, we prove the continuous dependence of the exact solution and its finite element approximations on data provided that the coeffici...