This book presents a unified theory of the Finite Element Method and the Boundary Element
Method for a numerical solution of second order elliptic boundary value problems. This …

The FEniCS Project set out in 2003 with an idea to automate the solution of mathematical
models based on differential equations. Initially, the FEniCS Project consisted of two …

Tearing and interconnecting methods, such as FETI, FETI-DP, BETI, etc., are among the
most successful domain decomposition solvers for partial differential equations. The …

A method is presented to include irregular domain boundaries in a geometric multigrid
solver. Dirichlet boundary conditions can be imposed on an irregular boundary defined by a …

The paper presents a multi-GPU implementation of the preconditioned conjugate gradient
algorithm with an algebraic multigrid preconditioner (PCG-AMG) for an elliptic model …

Multigrid methods are among the fastest numerical algorithms for the solution of large
sparse systems of linear equations. While these algorithms exhibit asymptotically optimal …

Domain decomposition (DD) methods provide powerful tools for constructing parallel
numerical solution algorithms for large scale systems of algebraic equations arising from the …

In this paper, we consider a monolithic approach to handle coupled fluid–structure
interaction problems with different hyperelastic models in an all-at-once manner. We apply …

This review study gives a widespread overview of the solutions of several engineering
problems based on some multidimensional partial differential equations like parabolic …

Multigrid (MG) methods are presented for fast, efficient, flexible, and robust least-squares
wavefront reconstruction in extremely high-resolution conventional adaptive optics, or ExAO …