Supercomputing and Computation

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Solvers


The objective of this research is to investigate the combination of high-order accurate Krylov deferred correction (KDC) and discontinuous Galerkin (DG) methods for high-performance computing. High-order schemes are usually more efficient than lower order ones for long simulation times in a time-dependent problem, because they have very low numerical diffusion and allow for a coarse spatial mesh. C. W. Shu has shown that high-order schemes can resolve solution structures, which are impractically expensive to obtain for low-order ones. Recently, high-order numerical schemes have attracted increasing attention for exascale computing because of their high computation intensity and efficient use of memory.

Related Projects

1-2 of 2 Results
 

Multiresolution and Adaptive Numerical Environment for Scientific Simulations (MADNESS)
— Numerical modeling softwares and solvers are key components of successful and accurate simulations for effective predictions and analysis. The results help us to improve our scientific theories as well as product and engineering designs. A representative of the most successful of the traditional software and solver environment is MATLAB with a core that is based on matrix and vector operations.

Scalable stencil-based solver algorithms
— This research concentrates on developing highly scalable algorithms and modular software in support of numerical methods for solving partial differential equations with stencil-based discretization approaches. Stencil codes require only nearest neighbor information in order to perform a numerical update and are thereby amenable to efficient and hybrid parallelization.

 
 
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