Sparse matrix LU decomposition method based on GPU

Abstract

The invention provides a sparse matrix LU decomposition method based on a GPU. The sparse matrix LU decomposition method includes the following steps: A, building a to-be-simulated circuit matrix of a circuit network on a CPU, and performing preprocessing and rarefaction on the circuit matrix; B, selecting a computing platform for processing a sparse matrix LU according to preprocessing results; C, performing decomposition on the sparse matrix LU through the GPU if the computing platform which is used is the GPU; D, performing back substitution solution on values of non-zero elements in the sparse matrix LU through the CPU so as to complete decomposition of the sparse matrix LU. According to the sparse matrix LU decomposition method, the computing platform can be selected automatically according to the number of floating-point operation times in decomposition, the task on the CPU and the task on the GPU can be distributed reasonably, coordinated operation of a plurality of threads on the GPU is guaranteed, and therefore the computing speed is improved and circuit simulation time is shortened.

Description

technical field [0001] The invention relates to the fields of electronic design automation and parallel computing, in particular to a GPU-based sparse matrix LU decomposition method. Background technique [0002] Sparse matrix LU decomposition is a basic operation in linear algebra, and it is widely used in circuit simulation, structural mechanics, economic modeling and many other fields. In circuit simulation, the circuit is represented as a matrix, and the circuit matrix is ​​extremely sparse, usually with only about 5 non-zero elements in each row. determined for this reason. The process of solving the circuit is the process of solving the sparse matrix equation Ax=b by using the sparse matrix LU decomposition. In a circuit simulation, the sparse matrix LU decomposition is located in the two-layer loop of Newton-Raphson iteration and transient iteration, and needs to be iteratively performed many times. This step is currently the most commonly used circuit simulation SP...

AI Technical Summary

Problems solved by technology

Since the number of CPU cores for shared memory is usually limited (most commercial CPUs do not exceed 6 cores, such as Intel Xeon X5680, AMD Phenom II), the performance of sparse matrix LU decomposition on multi-core CPUs cannot be further improved

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