Additive Operator Decomposition and Optimization–Based Reconnection with Applications

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Abstract

We develop an optimization-based approach for additive decomposition and reconnection of algebraic problems arising from discretizations of partial differential equations (PDEs). Application to a scalar convection–diffusion PDE illustrates the new approach. In particular, we derive a robust iterative solver for convection–dominated problems using standard multilevel solvers for the Poisson equation.