In this paper we address several topics relating to the development and implementation of volume integral and hybrid finite element methods for electromagnetic modeling. Comparisons with the finite elementboundary integral method are given in terms of accuracy and computing resources. We also discuss preconditioning, parallelization of the multilevel fast multipole method and propose higher-ord...

The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Optimal error estimates in L2 are established for the state...

A hierarchical multilevel preconditioner is constructed for an efficient solution of a first kind boundary integral equation with the single layer potential operator discretized by a boundary element method. This technique is based on a hierarchical clustering of all boundary elements as used in fast boundary element methods. This hierarchy is applied to define a sequence of nested boundary ele...

Using finite element methods, we need to answer these questions: • What is the appropriate functional space V for the solution? • What is the appropriate weak or variational form of a differential equation? • What kind of basis functions or finite element spaces should we choose? • How accurate is the finite element solution? We briefly address these questions in this Chapter. Recalling that fi...

In this paper, the boundary-based estimation of pressure distribution in the cardiovascular system is investigated using two dimensional flow images. The conventional methods of non-invasive estimation of pressure distribution in the cardiovascular flow domain use the differential form of governing equations. This study evaluates the advantages of using the integral form of the equations in the...

This paper is concerned with weak solution of a mixed boundary value problem for the biharmonic equation in the plane. Using Green’s formula, the problem is converted into a system of Fredholm integral equations for the unknown data on different part of the boundary. Existence and uniqueness of the solutions of the system of boundary integral equations are established in appropriate Sobolev spa...