SCREMS: High order numerical algorithms and their applications

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This award provides funds to secure computer equipment with initial setup and maintenance to support the computational requirements of several NSF supported projects, including algorithm design and application of high order numerical methods for convection dominated problems and high order numerical methods for elasticity, and numerical relativity. The algorithms being investigated include the finite difference and finite volume WENO schemes, discontinuous Galerkin and other finite element methods, and spectral methods, especially in adaptive, multiscale and uncertain environments. A particular emphasis of some of the proposed work is development and algorithmic adaptation of high-order methods to graphics processing unit (GPU) accelerated architectures. The algorithms developed in this project will help to improve our capability to understand the fundamental physics of many important problems, and to facilitate the engineering design and production of advanced materials, aircrafts, semiconductor devices, and energy products.