About

The Compadre Toolkit provides a performance portable solution for the parallel evaluation of computationally dense kernels. The toolkit specifically targets the Generalized Moving Least Squares (GMLS) approach, which requires the inversion of small dense matrices. The result is a set of weights that provide the information needed for remap or entries that constitute the rows of some globally sparse matrix.

This toolkit focuses on the 'on-node' aspects of meshless PDE solution and remap, namely the parallel construction of small dense matrices and their inversion. What it does not provide is the tools for managing fields, inverting globally sparse matrices, or neighbor search that requires orchestration over many MPI processes. This toolkit is designed to be easily dropped-in to an existing MPI (or serial) based framework for PDE solution or remap, with minimal dependencies (Kokkos and KokkosKernels).

Generalized Moving Least Squares (GMLS)

A GMLS problem requires the specification of a target functional $\tau$ (Compadre::TargetOperation), a reconstruction space $V$ (Compadre::ReconstructionSpace), and a sampling functional $\lambda$ (Compadre::SamplingFunctional).

The Compadre Toolkit is designed to efficiently assemble, factorize, and solve large batches of minimization problems having the form:

$\\ \begin{align*} p^{*}& =& \underset{p \in V}{\text{arg min}}\;\frac{1}{2}\sum_{j=1}^N (\lambda_j(u)-\lambda_j(p))^{2}\omega(\tau;\lambda_j)\\\\ &&\tau(u) \approx \tau(p^{*}) \end{align*}$