Spectral transform solutions to the shallow water test set
Journal of Computational Physics
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Smooth surface reconstruction from noisy range data
Proceedings of the 1st international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Climate Modeling with Spherical Geodesic Grids
Computing in Science and Engineering
Radial Basis Functions
Radial basis function interpolation: numerical and analytical developments
Radial basis function interpolation: numerical and analytical developments
Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions
Journal of Computational Physics
IEEE Computer Graphics and Applications
Scattered node compact finite difference-type formulas generated from radial basis functions
Journal of Computational Physics
On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere
Journal of Computational Physics
A Stable Algorithm for Flat Radial Basis Functions on a Sphere
SIAM Journal on Scientific Computing
The use of PDE centres in the local RBF Hermitian method for 3D convective-diffusion problems
Journal of Computational Physics
Implementing sparse matrix-vector multiplication on throughput-oriented processors
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
Stable computation of multiquadric interpolants for all values of the shape parameter
Computers & Mathematics with Applications
Fast Construction of k-Nearest Neighbor Graphs for Point Clouds
IEEE Transactions on Visualization and Computer Graphics
Concurrency and Computation: Practice & Experience - Proceedings of the 6th ACES Symposium, May 11–16, 2008, Cairns, Australia
Interactive SPH simulation and rendering on the GPU
Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Stabilization of RBF-generated finite difference methods for convective PDEs
Journal of Computational Physics
Keeneland: Bringing Heterogeneous GPU Computing to the Computational Science Community
Computing in Science and Engineering
Stable Computations with Gaussian Radial Basis Functions
SIAM Journal on Scientific Computing
Fast GPU-based locality sensitive hashing for k-nearest neighbor computation
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Journal of Computational Physics
Radial Basis Function Networks GPU-Based Implementation
IEEE Transactions on Neural Networks
Journal of Computational Physics
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This paper presents parallelization strategies for the radial basis function-finite difference (RBF-FD) method. As a generalized finite differencing scheme, the RBF-FD method functions without the need for underlying meshes to structure nodes. It offers high-order accuracy approximation and scales as O(N) per time step, with N being with the total number of nodes. To our knowledge, this is the first implementation of the RBF-FD method to leverage GPU accelerators for the solution of PDEs. Additionally, this implementation is the first to span both multiple CPUs and multiple GPUs. OpenCL kernels target the GPUs and inter-processor communication and synchronization is managed by the Message Passing Interface (MPI). We verify our implementation of the RBF-FD method with two hyperbolic PDEs on the sphere, and demonstrate up to 9x speedup on a commodity GPU with unoptimized kernel implementations. On a high performance cluster, the method achieves up to 7x speedup for the maximum problem size of 27,556 nodes.