Algebraic Multigrid Schemes for High-Order Nodal Discontinuous Galerkin Methods
Paola F. Antonietti, Laura Melas
Abstract
We present algebraic multigrid (AMG) methods for the efficient solution of the linear system of equations stemming from high-order discontinuous Galerkin (DG) discretizations of second-order elliptic problems. For DG methods, standard multigrid approaches cannot be employed because of redundancy of the degrees of freedom associated to the same grid point. We present new aggregation procedures and test them in extensive two-dimensional numerical experiments to demonstrate that the proposed AMG method is uniformly convergent with respect to all of the discretization parameters, namely the mesh-size and the polynomial approximation degree.
Topics & Concepts
Multigrid methodMathematicsDiscretizationDiscontinuous Galerkin methodGalerkin methodApplied mathematicsDegree of a polynomialPolynomialGridElliptic curveFinite element methodMathematical analysisPartial differential equationGeometryThermodynamicsPhysicsAdvanced Numerical Methods in Computational MathematicsComputational Fluid Dynamics and AerodynamicsAdvanced Mathematical Modeling in Engineering