An optimization-based, heterogeneous to homogeneous coupling method

An optimization based heterogeneous to homogeneous coupling method

An optimization based algorithm is proposed for solving elliptic problems with highly oscillatory coefficients that do not exhibit scale separation in a subregion of the physical domain. The given method, written as a constrained minimization problem couples a numerical homogenization method in the subregion of the physical domain with scale separation with a fine scale solver in subregions wit...

An optimization-based multiscale coupling method

An optimization based algorithm is proposed for solving elliptic problems with highly oscillatory coefficients that do not exhibit scale separation in a subregion of the physical domain. The given method, written as a constrained minimization problem couples a numerical homogenization method in the subregion of the physical domain with scale separation with a fine scale solver in subregions wit...

Development of an Optimization-Based Atomistic-to-Continuum Coupling Method

Atomistic-to-Continuum (AtC) coupling methods are a novel means of computing the properties of a discrete crystal structure, such as those containing defects, that combine the accuracy of an atomistic (fully discrete) model with the efficiency of a continuum model. In this note we extend the optimization-based AtC, formulated in [17] for linear, one-dimensional problems to multi-dimensional set...

An Optimization Based Coupling Method for Multiscale Problems

Converting homogeneous to heterogeneous catalysts

Homogeneous transition metal complex catalysts for organic industrial processes are converted to catalysts which are heterogeneous with respect to the reactants, and which have substantially equal catalytic activity to the homogeneous catalysts. This is done by reacting a normally homogeneous transition metal complex catalyst with a metal bridging ligand which substantially duplicates the ligan...