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289views
7 years 6 months ago
An Analysis of Finite Volume, Finite Element, and Finite Difference Methods Using Some Concepts from Algebraic Topology
In this paper we apply the ideas of algebraic topology to the analysis of the finite volume and finite element methods, illuminating the similarity between the discretization str...
Claudio Mattiussi

Publication
519views
7 years 6 months ago
The Finite Volume, Finite Difference, and Finite Elements Methods as Numerical Methods for Physical Field Problems
I. Introduction II. Foundations A. The Mathematical Structure of Physical Field Theories B. Geometric Objects and Orientation 1. Space-Time Object...
Claudio Mattiussi

Publication
216views
7 years 6 months ago
The Geometry of Time-Stepping
The space-time geometric structure of Maxwell’s equations is examined and a subset of them is found to define a pair of exact discrete time-stepping relations. The desirability ...
Claudio Mattiussi

Publication
338views
7 years 6 months ago
A Reference Discretization Strategy for the Numerical Solution of Physical Field Problems.
I. Introduction II. Foundations A. The Mathematical Structure of Physical Field Theories B. Geometric Objects and Orientation 1. Space-Time Object...
Claudio Mattiussi
ICASSP
2011
IEEE
8 years 3 days ago
Computing room acoustics with CUDA - 3D FDTD schemes with boundary losses and viscosity
In seeking to model realistic room acoustics, direct numerical simulation can be employed. This paper presents 3D Finite Difference Time Domain schemes that incorporate losses at ...
Craig J. Webb, Stefan Bilbao
MCM
2010
8 years 3 months ago
Electromagnetic interrogation and the Doppler shift using the method of mappings
We consider the electromagnetic detection of hidden moving or oscillating conductive targets. The resulting mathematical problem involves computation of a Doppler shift for an ele...
H. T. Banks, Shuhua Hu, W. Clayton Thompson
ICPP
2009
IEEE
9 years 3 months ago
Mapping the FDTD Application to Many-Core Chip Architectures
—This paper reports a study of mapping the Finite Difference Time Domain (FDTD) application to the IBM Cyclops64 (C64) many-core chip architecture [1]. C64 is chosen for this stu...
Daniel Orozco, Guang R. Gao
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