V.S. Melikyan1, E.S. Ghazaryan2, A.G. Harutyunyan3

1–3 National Polytechnic University of Armenia (Yerevan, Armenia)
1 CJSC Synopsys Armenia (Yerevan, Armenia)
1 vazgenm@synopsys.com, 2 eghazaryan911@gmail.com, 3 harash@seua.am

Problem Statement. Accurate and efficient circuit modeling is crucial in modern electronics. A key part of circuit simulation is solving large systems of linear equations generated using Modified Nodal Analysis (MNA), where circuit behavior is represented through Kirchhoff's laws. Efficient and accurate numerical solvers are essential, especially for large-scale circuits with varying sparsity and condition numbers. The challenge lies in selecting an appropriate solver that balances computational efficiency, memory usage, and accuracy based on matrix properties such as symmetry, sparsity, condition number, and size.

Objective. The main goal of this work is a comparative analysis of four numerical solvers: LU decomposition, Sparse LU, Conjugate Gradient (CG), and an adaptive method combining CG and Sparse LU. The evaluation is based on performance and accuracy analysis using C++ Eigen library solvers, considering execution time, memory consumption, and numerical accuracy.

Results. Direct solvers (LU, Sparse LU) provide high accuracy but suffer from high computational and memory costs, making them impractical for large circuits. Sparse LU improves efficiency by leveraging matrix sparsity, making it a preferable choice when exact solutions are required. Iterative solvers, particularly CG, exhibit superior scalability for highly sparse systems, achieving the lowest execution times. The Adaptive method dynamically switches between CG and Sparse LU, offering a balance between efficiency and accuracy.

Practical Significance. The obtained results enable engineers to make correct decisions when selecting solvers based on their circuit characteristics, ensuring both computational efficiency and numerical reliability.

Melikyan V.S., Ghazaryan E.S., Harutyunyan A.G. Performance and accuracy analysis of linear solvers in circuit-level simulation. Dynamics of complex systems. 2025. V. 19. № 2. P. 7–11. DOI: https://doi.org/10.18127/j19997493-202502-02 [in Russian]

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