Optimized CUDA-Based PDE Solver for Reaction Diffusion Systems on Arbitrary Surfaces

Partial differential equation (PDE) solvers are commonly employed to study and characterize the parameter space for reaction-diffusion (RD) systems while investigating biological pattern formation. Increasingly, biologists wish to perform such studies with arbitrary surfaces representing ‘real’ 3D geometries for better insights. In this paper, we present a highly optimized CUDA-based solver for RD equations on triangulated meshes in 3D. We demonstrate our solver using a chemotactic model that can be used to study snakeskin pigmentation, for example. We employ a finite element based approach to perform explicit Euler time integrations. We compare our approach to a naive GPU implementation and provide an in-depth performance analysis, demonstrating the significant speedup afforded by our optimizations. The optimization strategies that we exploit could be generalized to other mesh based processing applications with PDE simulations.

Efficient algorithms for solving systems of ordinary differential equations for ecosystems modeling /

Mode of access: Internet.

A dictionary of chemical equations.

Mode of access: Internet.

Partial differential equations.

Mode of access: Internet.

An investigation of the exact solutions of the linearized equations for the flow past conical bodies,

Reproduced from type-written copy.

Existence theorems in partial differential equations.

"Only the material on elliptic equations will appear in these notes."

Integral equations

Mode of access: Internet.

Differential equations; geometric theory.

Mode of access: Internet.

Partial differential equations,

Mimeographed.

A computer research program for solving the reaction rate equations in the E ionospheric region /

Ionospheric Physics Laboratory Project 8653.

Plane waves and spherical means applied to partial differential equations.

Bibliography: p. 165-170.

Forecasting auto ownership and mode choice for U.S. metropolitan areas. Volume II: model equations. Final report.

Transportation Department, Office of University Research, Washington, D.C.

Numerical integrators for stiff and highly oscillatory differential equations /

Bibliography: p. 27-28.

An automatic integrator for ordinary differential equations for ILLIAC IV /

"June 1, 1969."

Error estimation and iterative improvement for the numerical solution of operator equations /

Bibliography: p. 85-87.