Abstract
Sparse matrix-vector multiplication (SpMV) can be used to solve diverse-scaled linear systems and eigenvalue problems that exist in numerous, and varying scientific applications. One of the scientific applications that SpMV is involved in is known as Configuration Interaction (CI). CI is a linear method for solving the nonrelativistic Schrödinger equation for quantum chemical multi-electron systems, and it can deal with the ground state as well as multiple excited states. In this paper, we have developed a hybrid approach in order to deal with CI sparse matrices. The proposed model includes a newly-developed hybrid format for storing CI sparse matrices on the Graphics Processing Unit (GPU). In addition to the new developed format, the proposed model includes the SpMV kernel for multiplying the CI matrix (proposed format) by a vector using the C language and the Compute Unified Device Architecture (CUDA) platform. The proposed SpMV kernel is a vector kernel that uses the warp approach. We have gauged the newly developed model in terms of two primary factors, memory usage and performance. Our proposed kernel was compared to the cuSPARSE library and the CSR5 (Compressed Sparse Row 5) format and already outperformed both.
Highlights
A Graphics Processing Unit (GPU) is an electronic chip that is designed for extremely fast parallel computations and processing of data
We are proposing a new model for storing Configuration Interaction (CI) sparse matrices on the GPU
We have implemented the kernel of the Sparse matrix-vector multiplication (SpMV) operation for the proposed model
Summary
A Graphics Processing Unit (GPU) is an electronic chip that is designed for extremely fast parallel computations and processing of data. The constant memory can be accessed by by all the threads within the grid, just like the global memory. The CPU launches on the GPU multiple copies of the kernel on parallel threads to process the GPU data. The following code is a simple GPU kernel (written in CUDA) called AddArrays that is used for the purpose of adding two integer arrays In this case, the CPU launches on the GPU multiple copies of the AddArrays kernel on parallel threads (one kernel per thread) in order to perform the addition operation. CUDA allows us to run millions of threads or more, programs that run on the GPU aren’t million times faster than the CPU for multiple reasons: It takes time to copy data from the CPU to the GPU and vice versa. As a matter of fact, improving the SpMV operation is extremely critical to the performance of a variety of scientific applications
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