To evaluate the computational performance of high-order elements, a comparison based on operation count is proposed instead of runtime comparisons. More specifically, linear versus high-order approximations are analyzed for implicit solver under a standard set of hypotheses for the mesh and the solution. Continuous and discontinuous Galerkin methods are considered in two-dimensional and three-dimensional domains for simplices and parallelotopes. Moreover, both element-wise and global operations arising from different Galerkin approaches are studied. The operation count estimates show, that for implicit solvers, high-order methods are more efficient than linear ones.
Abstract
To evaluate the computational performance of high-order elements, a comparison based on operation count is proposed instead of runtime comparisons. [...]
Three Galerkin methods-continuous Galerkin, Compact Discontinuous Galerkin, and hybridizable discontinuous Galerkin-are compared in terms of performance and computational efficiency in 2-D scattering problems for low and high-order polynomial approximations. The total number of DOFs and the total runtime are used for this correlation as well as the corresponding precision. The comparison is carried out through various numerical examples. The superior performance of high-order elements is shown. At the same time, similar capabilities are shown for continuous Galerkin and hybridizable discontinuous Galerkin, when high-order elements are adopted, both of them clearly outperforming compact discontinuous Galerkin. hree Galerkin methods—continuous Galerkin, Compact Discontinuous Galerkin, and hybridizable discontinuous Galerkin—are compared in terms of performance and computational efficiency in 2-D scattering problems for low and high-order polynomial approximations. The total number of DOFs and the total runtime are used for this correlation as well as the corresponding precision. The comparison is carried out through various numerical examples. The superior performance of high-order elements is shown. At the same time, similar capabilities are shown for continuous Galerkin and hybridizable discontinuous Galerkin, when high-order elements are adopted, both of them clearly outperforming compact discontinuous Galerkin
Abstract
Three Galerkin methods-continuous Galerkin, Compact Discontinuous Galerkin, and hybridizable discontinuous Galerkin-are compared in terms of performance [...]
Efficiency of high-order elements for continuous and discontinuous Galerkin methods 