Parallel Multi-Rate Circuit Simulation Using Hybrid Matrix Partitioning
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Solution Overview
Problem
Current circuit simulation methods face inefficiencies in parallel computation due to the bottleneck of LU decomposition, particularly in large, sparse circuit simulation matrices, which leads to slow convergence and high memory usage when applying Krylov-subspace methods at the top level.
Innovation Solution
A hybrid direct and iterative method is introduced, where the circuit Jacobian matrix is partitioned into loosely coupled blocks, reordered, and split into matrices M and N, with M being suitable for parallel processing and N serving as a coupling matrix, allowing for preconditioning and iterative solving to accelerate convergence.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If Krylov-subspace methods are applied at the top level of circuit simulation matrices, then convergence is achieved, but memory usage increases and computational overhead increases
Solution Approach 1:
The circuit simulation matrix is segmented into subsystems using Schur complement decomposition. The top-level matrix is divided into block diagonal subsystems that can be solved independently with reduced memory requirements, while maintaining convergence through iterative coupling of the subsystems.
2Measurement precision
If LU decomposition is performed on large circuit simulation matrices, then accurate solutions are obtained, but fill-ins increase and computational overhead increases
Solution Approach 1:
The large circuit matrix is segmented into block diagonal subsystems via Schur complement decomposition. Each subsystem undergoes LU decomposition independently, significantly reducing fill-ins compared to decomposing the full dense top-level matrix, while maintaining solution accuracy through iterative refinement.
3Productivity
If parallel processing is applied to circuit simulation, then computational speed increases, but the bottleneck of LU decomposition limits scalability
Solution Approach 1:
The circuit simulation problem is segmented into independent block diagonal subsystems that can be processed in parallel. Each subsystem is solved independently using LU decomposition, eliminating the scalability bottleneck of traditional parallel LU decomposition on the full matrix while maintaining computational speed through efficient parallel execution of subsystems.
Data Source
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AI summary
A computer-implemented method for solving parallel equations in a circuit simulation is described. The method includes partitioning a circuit Jacobian matrix into loosely coupled partitions, reordering the voltage vector and the matrix according to the partitions, and splitting the Jacobian matrix into two matrices M and N, where M is a matrix suitable for parallel processing and N is a coupling matrix. M and N are then preconditioned to form M