A numerical homogenization method is here presented to solve problems governed by partial differential equations with coefficients that are generic functions in $R^2$. It consists of a recursive finite elements discretization and an algebraic homogenization. This method takes advantages for speed and memory occupation from the hierarchy of elements and nodes defined by the recursive discretization. It turns out that using state-of-the-art general linear algebra techniques, all non-numerical data manipulations that are typically done before real computations, can be avoided.
A Fast Numerical Homogenization Algorithm for Finite Element Analysis
MARCUZZI, FABIO
1999
Abstract
A numerical homogenization method is here presented to solve problems governed by partial differential equations with coefficients that are generic functions in $R^2$. It consists of a recursive finite elements discretization and an algebraic homogenization. This method takes advantages for speed and memory occupation from the hierarchy of elements and nodes defined by the recursive discretization. It turns out that using state-of-the-art general linear algebra techniques, all non-numerical data manipulations that are typically done before real computations, can be avoided.
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