Microstructural Decomposition Error Estimates

Abstract

AbstractComputational simulations of interacting microstructure in solid structures, with methods such as the finite element method, require solutions to numerically enormous boundary value problems. The primary objective of this work is to introduce a‐posteriori error bounds for a domain decomposition which can be used to reduce the computational complexity of boundary value problems associated with such simulations. The approach is to partition and decouple the heterogeneous body into more computationally tractable, nonoverlapping, subdomains whose union forms the entire domain under analysis. This is achieved by computing a relatively inexpensive auxiliary „decoupling problem”︁ with regularized coefficients but with the same external geometry and loading as the original body. The solution to the decoupling problem is then used to construct local boundary data for the subdomains, which can thereafter be solved independently, possibly in parallel.