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High performance finite difference PDE solvers on GPUs

Daniel Egloff
QuantAlea GmbH
Technical report, QuantAlea GmbH, February 2010

@techreport{egloff2010high,

   title={High performance finite difference PDE solvers on GPUs},

   author={Egloff, D.},

   year={2010},

   institution={Technical Report, QuantAlea Gmbh}

}

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We show how to implement highly efficient GPU solvers for one dimensional PDEs based on finite difference schemes. The typical use case is to price a large number of similar or related derivatives in parallel. Application scenarios include market making, real time pricing, and risk management. The tridiagonal systems in the backward propagation of a finite difference scheme are solved with parallel cyclic reduction. This is a fine-grained parallel tridiagonal solver, which is well adapted to the hierarchical architecture of a modern GPU. We explain in detail the calculation work flow and study the performance of the solver relative to a well optimized CPU implementation. Our timings demonstrate performance improvement factors 25 on a single GPU and 38 on two GPUs.
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