101. Effective conductivity by a probability-based local method.
- Author
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Grigoriu, Mircea and Papoulia, Katerina D.
- Subjects
- *
MATERIALS , *MONTE Carlo method , *STOCHASTIC processes , *NUMERICAL analysis , *ALGORITHMS , *PHYSICS - Abstract
A local method is developed for estimating the effective conductivity for materials with varying deterministic or random conductivity on domains with mixed boundary conditions. The effective conductivity is the conductivity of a virtual homogeneous material which behaves globally as the original heterogeneous material. It is shown that the effective conductivity can be calculated from the values of the potential at a relatively small number of points in the specimen. A method is developed for calculating the potential at an arbitrary point in the specimen directly, rather than extracting its value from a field solution. The method is based on some technical concepts related to properties of diffusion processes and an extension of Itô’s formula for continuous semimartingales to the case of reflected diffusion processes. However, the application of the method is intuitive and uses elementary Monte Carlo simulation algorithms. The paper presents essential facts proving the validity of the proposed method and two numerical examples illustrating the calculation of the effective conductivity for specimens with deterministic and random conductivity fields. [ABSTRACT FROM AUTHOR]
- Published
- 2005
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