Parallel Implementation Of Field Visualizations With High Order Tetrahedral Finite Elements

In the adaptive finite element method (AFEM), high order finite elements are usually used in the computations. In three dimensional simulations, post-processing poses considerable challenge since available data visualization software programs do not accommodate such a high order visualization—common data visualizers can only visualize for up to ten-node tetrahedron elements. This work proposes and implements an efficient framework for data visualization with tetrahedron finite elements having hierarchical basis functions. A general method for post-processing of field data with high order tetrahedra is presented. The method builds upon an approach of the open source visualization software VTK where the data visualizer program ParaView is freely available. By using Red Partitioning of high order elements, the implemented algorithm successfully enables visualization of up to fourth order tetrahedra while using the same data structure for second order tetrahedra as available in ParaView. The results of the implementation clearly show the corresponding increase in accuracy of visualization when the polynomial orders were increased, i.e., the field contour lines are increasingly smoother. Parallelism of the code with the message passing package openMPI was also implemented to increase the computational performance in a multicore computing platform. The results show that computational times taken in the data post-processing significantly decreases when multicore parallel processing is enabled. The developed algorithm was assessed on various problem geometries with considerable high number of unknowns where it is found that the approach is quite scalable

Well-balanced energy-stable residual distribution methods for the shallow water equations with varying bottom topography

This paper presents an alternative well-balanced and energy stable method for the system of non-homogeneous Shallow Water Equations (SWE) on unstructured grids based on the residual distribution (RD) approach. The motivation of the work is based on the grid insensitivity of RD method. The newly proposed method has a positive first order part, a linearity-preserving second order scheme as well as a limited scheme which works for both steady and unsteady problems using simple, explicit time integration techniques. Numerical results herein confirm the accuracy and efficacy of the new methods in preserving both energy stability and well-balancedness