Efficient implementation of the Localized Orthogonal Decomposition method
For researchers in numerical simulation of multiscale PDEs, this work provides practical implementation strategies for a known method, but is incremental in nature.
The paper presents algorithms for efficiently implementing the Localized Orthogonal Decomposition method for multiscale PDEs, enabling its use in standard finite element frameworks for problems like rough-coefficient elliptic and eigenvalue problems.
In this paper we present algorithms for an efficient implementation of the Localized Orthogonal Decomposition method (LOD). The LOD is a multiscale method for the numerical simulation of partial differential equations with a continuum of inseparable scales. We show how the method can be implemented in a fairly standard Finite Element framework and discuss its realization for different types of problems, such as linear elliptic problems with rough coefficients and linear eigenvalue problems.