The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

In this short note, we present a new technique to accelerate the convergence of a FFT-based
solver for numerical homogenization of complex periodic media proposed by Moulinec and …

When solving elliptic boundary value problems using integral equation methods one may
need to evaluate potentials represented by a convolution of discretized layer density …

In this paper, the standard and the localized space‐time radial basis function (RBF)
collocation methods are modified and combined with the time‐marching scheme and space …

We take a fairly comprehensive approach to the problem of solving elliptic partial differential
equations numerically using integral equation methods on domains where the boundary has …

We present a method for solving Poisson and heat equations with discontinuous coefficients
in two-and three-dimensions. It uses a Cartesian cut-cell/embedded boundary method to …

In recent years the traditional subject of continuum mechanics has grown rapidly and many
new techniques have emerged. This text provides a rigorous, yet accessible introduction to …

Guaranteed upper–lower bounds on homogenized coefficients, arising from the periodic cell
problem, are calculated in a scalar elliptic setting. Our approach builds on the recent …

We present a review of some of the state-of-the-art numerical methods for solving the Stefan
problem and the Poisson and the diffusion equations on irregular domains using (i) the level …

This paper presents an exact solution for steady-state conduction heat transfer in cylindrical
composite laminates. This laminate is cylindrical shape and in each lamina, fibers have …