Improving Algebraic Multigrid Performance for High-order Finite Elements with Multipoint Constraints
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The main goal of high-fidelity structural analyses is recovering a detailed stress field, which makes high-order element formulations particularly appealing. In an effort to reduce the complexity of large assemblies, multipoint constraints are often used to represent subcomponents. Since these large problems are too big for direct solvers, they are usually solved with iterative algebraic multigrid solvers. However, traditional AMG (algebraic multigrid) solvers are ill-equipped to handle linear systems produced by high-order finite elements efficiently. An option to improve their performance is exploiting the high-order formulations to perform optimal coarsening on the first few levels. Nevertheless, such methods have limitations, such as failing to handle multipoint constraints. In this work, we extend the hybrid geometric-algebraic multigrid linear solver with support for multipoint constraints. Benchmark cases comparing the performance of existing methods to the proposed one are studied.
