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For fifty years, improvements in transistor speed, efficiency, and reduction in their size drove the improvements in computer hardware that society has come to rely on. The pace of such improvements is increasingly costly to sustain.
One way to offer higher performance and better efficiency in computer hardware going forward is through specialization. Specialized hardware for rendering graphics, encryption, and pattern recognition are now at the forefront of our techniques for extracting greater capability from existing computer hardware.
In this project, you will investigate how specialized computer hardware can tackle important problems in scientific simulations.
In this project you will first review how scientific simulations are phrased as partial differential equations (PDEs). Researchers then use a well-studied set of algorithms call numerical integrators (Euler's method, Lax-Wendroff methods, for example) to find solutions to those partial differential equations. After reviewing PDEs and integration methods, in this project you will consider various options for encoding those algorithms as a simple set of hardware rules, creating a hardware design that is specialized for solving PDEs.
This interdisciplinary project will provide excellent exposure to topics in applied mathematics, algorithms, high performance computing (supercomputers), and techniques for developing digital hardware designs.
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