DIRECTFN: Fully Numerical Algorithms for High Precision Computation of Singular Integrals in Galerkin SIE Methods
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This paper investigates the particular problem of matrices appearing during the modeling of Integrated Circuits with Finite Integration Technique (FIT) method. We present the key points of FIT approach followed by an illustration of the structure and the p ...
The present report addresses the rigorous study of convergence of a stabilized finite volume element method applied to stationary and time dependent Stokes problems. Some preliminary results about the existence and uniqueness of solution at continuous and ...
A magnet is a pair u, v of adjacent vertices such that the proper neighbours of u are completely linked to the proper neighbours of v. It has been shown that one can reduce the graph by removing the two vertices u, v of a magnet and introducing a new verte ...
Engineers rely on efficient simulations that provide them with reliable data in order to make proper engineering design decisions. The purpose of this thesis is to design adaptive numerical methods for multiscale problems in this spirit. We consider ellipt ...
An alternative analytical approach to calculate the weakly singular free-space static potential integral associated to uniform sources is presented. Arbitrary oriented flat polygons are considered as integration domains. The technique stands out by its mat ...
The direct evaluation program tailored to the singular integrals arising in the first-kind and second-kind Fredholm surface integral equation formulations is presented. The exponential convergence of the proposed technique can safely guarantee the inherite ...
Surface Mixed Potential Integral Equation (MPIE) formulations together with the Method of Moments (MoM) are widely used to solve electromagnetic problems. An accurate evaluation of the Green functions (GF) associated to the integral equation and of the cou ...
Extensions and variations of the basic problem of graph coloring are introduced. The problem consists essentially in finding in a graph G a k-coloring, i.e., a partition V-1,...,V-k of the vertex set of G such that, for some specified neighborhood (N) over ...
Novel generalized Cartesian product rules for the computation of weakly singular integrals, arising in the mixed potential integral equation formulations are presented in this paper. The key feature of the proposed integration schemes lies in the incorpora ...
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Starting from the basic problem of reconstructing a 2-dimensional image given by its projections on two axes, one associates a model of edge coloring in a complete bipartite graph. The complexity of the case with k=3 colors is open. Variations and special ...