Element-Free AMGe: General Algorithms for Computing Interpolation Weights in AMG

• Published in: SIAM journal on scientific computing Vol. 23; no. 2; pp. 629 - 650
• Main Authors: Henson, Van Emden, Vassilevski, Panayot S.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 2002
• Subjects: Algebra; Algorithms; Boundary conditions; Exact sciences and technology; Laboratories; Mathematics; Neighborhoods; Numerical analysis; Numerical analysis. Scientific computation; Numerical linear algebra; Partial differential equations, boundary value problems; Sciences and techniques of general use; Sparsity; Harmonic; Freedom degree; Grid pattern; Mathematical operator; Mapping; Boundary value; Algorithm; Partial differential equation; Discretization method; Weight; Equation system; Ellipticity; Finite element method; Interpolation; Elliptic equation; Numerical computation; Multigrid; Linear algebra; Matrix calculus; Algebraic multigrid algorithm; Relaxation method; Gauss Seidel method; Algebraic geometry
• ISSN: 1064-8275; 1095-7197
• DOI: 10.1137/S1064827500372997

We propose anew general algorithm for constructing interpolation weights in algebraic multigrid (AMG). It exploits a proper extension mapping outside a neighborhood about a fine degree of freedom (dof) to be interpolated. The extension mapping provides boundary values (based on the coarse dofs used to perform the interpolation) at the boundary of the neighborhood. The interpolation value is then obtained by matrix dependent harmonic extension of the boundary values into the interior of the neighborhood. We describe the method, present examples of useful extension operators, provide a two-grid analysis of model problems, and, by way of numerical experiments, demonstrate the successful application of the method to discretized elliptic problems.