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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
SIAMNUM
2010
178views more  SIAMNUM 2010»
8 years 3 months ago
A New Class of High Order Finite Volume Methods for Second Order Elliptic Equations
In the numerical simulation of many practical problems in physics and engineering, finite volume methods are an important and popular class of discretization methods due to the loc...
Long Chen
PAAPP
2002
76views more  PAAPP 2002»
8 years 8 months ago
Performance of PDE solvers on a self-optimizing NUMA architecture
Abstract. The performance of shared-memory (OpenMP) implementations of three different PDE solver kernels representing finite difference methods, finite volume methods, and spectra...
Sverker Holmgren, Markus Nordén, Jarmo Rant...
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