Finite Element Network Approximation of Conductivity in Particle Composites
Please always quote using this URN:urn:nbn:de:0296-matheon-9137
- A new finite element method computes conductivity in some unstructured particle-reinforced composite material. The 2-phase material under consideration is composed of a poorly conducting matrix material filled by highly conducting circular inclusions which are randomly dispersed. The mathematical model is a Poisson-type problem with discontinuous coefficients. The discontinuities are huge in contrast and quantity. The proposed method generalizes classical continuous piecewise affine finite elements to special computational meshes which encode the particles in a network structure. Important geometric parameters such as the volume fraction are preserved exactly. The computational complexity of the resulting method is proportional to the number of inclusions and this is optimal in comparison to data complexity. The discretization error is proportional to the particle distance and does not depend on the conductivity contrast in the medium.
Author: | Daniel Peterseim, Carsten Carstensen |
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URN: | urn:nbn:de:0296-matheon-9137 |
Referee: | Harry Yserentant |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2011/11/10 |
Release Date: | 2011/11/10 |
Tag: | discrete network; finite elements; high contrast; micro-structure |
Institute: | Research Center Matheon |
Humboldt-Universität zu Berlin | |
Project: | C Energy and Materials (Production) |
MSC-Classification: | 65-XX NUMERICAL ANALYSIS |
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems | |
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Qxx Homogenization, determination of effective properties / 74Q20 Bounds on effective properties | |
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Qxx Homogenization, determination of effective properties | |
Preprint Number: | 824 |