Immersed boundary methods for computing confined fluid and plasma flows in complex
geometries are reviewed. The mathematical principle of the volume penalization technique …

This book provides a comprehensive introduction to the subject of numerical analysis, which
is the study of the design, analysis, and implementation of numerical methods for solving …

Photonic crystal fibres are novel optical devices that can be designed to guide light of a
particular frequency. In this paper the performance of planewave expansion methods for …

An a posteriori error estimator is developed for the eigenvalue analysis of heterogeneous
elastic structures. It constitutes an extension of a well-known explicit estimator to …

We study the properties of an approximation of the Laplace operator with Neumann
boundary conditions using volume penalization. For the one-dimensional Poisson equation …

Diagonalized Legendre spectral methods for solving second-order eigenvalue problems are
proposed. A new class of basis functions are constructed by using the matrix decomposition …

In this paper we present an efficient spectral method based on the Legendre–Galerkin
approximation for the transmission eigenvalue problem. A rigorous error analysis is …

Consider a model eigenvalue problem with a piecewise constant coefficient. We split the
domain at the discontinuity of the coefficient function and define the multidomain variational …

We describe Fourier pseudospectral time-domain simulations, carried out in order to study
light interacting with a metallic nanoscale object. The difficulty of using Fourier methods to …

We report the results of a study on the spectral properties of Laplace and Stokes operators
modified with a volume penalization term designed to approximate Dirichlet conditions in the …