Development and Validation of In-house Iterative Solvers for Linear Systems in Implicit Structural Analysis Based on Lattice Models

Young Kwang Hwang; Jong-Chan Kim; Ki-Ha Kim

doi:10.7734/COSEIK.2025.38.4.279

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2025 Vol.38, Issue 4 Preview Page

Research Paper

Development and Validation of In-house Iterative Solvers for Linear Systems in Implicit Structural Analysis Based on Lattice Models 격자 모델 기반 내연적 구조해석을 위한 선형 시스템 반복 솔버 개발 및 검증

31 August 2025. pp. 279-286

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Abstract

In this study, a comprehensive suite of iterative solvers was developed to efficiently address linear systems arising from implicit time integration and nonlinear static analysis. The package incorporates several iterative solvers and preconditioning techniques to manage large and sparse matrices. In-house development was undertaken to enable flexibility in modifying and applying the program code for various structural problems. Furthermore, matrix and vector operations were implemented using the compressed sparse row (CSR) format, significantly reducing memory usage and improving computational efficiency. To validate the developed code, the solution algorithms were applied to linear systems formed from the stiffness matrices of a Voronoi-cell lattice model. Considering both linear and nonlinear static structural problems, the corresponding symmetric and asymmetric system matrices were constructed and utilized. In a practical application, the solution algorithms were applied to a beam deflection problem, and the numerical results obtained from the iterative methods were compared and evaluated in terms of convergence, computational efficiency, matrix symmetry, and system size. The results demonstrated the numerical robustness of the in-house iterative solvers and validated their applicability to implicit structural analysis problems.

Keywords

linear system

matrix solver

structural analysis

iterative method

implicit method

Krylov subspace

본 연구에서는 내연적 시간적분법과 비선형 정적해석에서 발생하는 선형 시스템을 효율적으로 해결하기 위한 자체 솔버 프로그램을 개발하고 이를 평가하였다. 희소행렬 연산에 유용한 반복법과 전처리기(preconditioner) 알고리즘을 구현하였으며, 자체 개발을 통해 프로그램 코드의 수정 및 활용을 용이하게 하였다. 또한 메모리 사용량 절감 및 계산 효율성 향상을 위해 CSR(compressed sparse row) 형식 기반의 행렬 및 벡터 연산을 구현하였다. 개발된 솔버 성능 검증을 위해 Voronoi-cell 격자 모델 기반 선형시스템을 대상으로 개별 반복법 알고리즘을 적용하였다. 아울러 선형/비선형 정적 구조 거동을 모두 고려하여 관련 대칭/비대칭 시스템 행렬을 도출하고 이를 활용하였다. 보의 처짐 문제를 대상으로 각 반복법의 결과를 수렴성, 계산 시간, 행렬의 대칭성 및 크기에 따라 비교 분석하였다. 이를 통해 자체 개발한 반복법 솔버의 수치적 성능을 검증하였고 내연적 구조해석 등에 수반되는 선형 시스템의 근사해 계산에 개발 코드를 효과적으로 활용할 수 있음을 확인하였다.

키워드

선형 시스템

행렬 솔버

구조해석

반복법

내연적 해석

크릴로프 부공간

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Information

Publisher :Computational Structural Engineering Institute of Korea
Publisher(Ko) :한국전산구조공학회
Journal Title :Journal of the Computational Structural Engineering Institute of Korea
Journal Title(Ko) :한국전산구조공학회 논문집
Volume : 38
No :4
Pages :279-286
Received Date : 2025-06-13
Revised Date : 2025-07-08
Accepted Date : 2025-07-08
DOI :https://doi.org/10.7734/COSEIK.2025.38.4.279

Journal of the Computational Structural Engineering Institute of Korea ISSN:1229-3059(Print) 2287-2302(Online) 한국전산구조공학회 논문집

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