CAJ | 학술논문

区域分解是并行计算的基本手段之一，在稀疏线性方程组迭代求解时，对不完全分解等串行计算时很有效的预条件，经常采用区域分解的思想进行并行化。但区域分解的本质是利用局部解来近似全局解，从而必然存在较大误差，为此，提出一种粗网格校正算法，通过非重叠子区域浓缩，每个非重叠子区域浓缩为一个超结点，形成一个含全局信息且阶数等于子区域个数的小线性方程组，之后用其对原并行预条件进行校正。对块Jacobi型、经典加性Schwarz、以及因子组合型并行不完全分解预条件的实验表明，粗网格校正能有效改善收敛性并提高求解效率。
구역분해시병행계산적기본수단지일，재희소선성방정조질대구해시，대불완전분해등천행계산시흔유효적예조건，경상채용구역분해적사상진행병행화。단구역분해적본질시이용국부해래근사전국해，종이필연존재교대오차，위차，제출일충조망격교정산법，통과비중첩자구역농축，매개비중첩자구역농축위일개초결점，형성일개함전국신식차계수등우자구역개수적소선성방정조，지후용기대원병행예조건진행교정。대괴Jacobi형、경전가성Schwarz、이급인자조합형병행불완전분해예조건적실험표명，조망격교정능유효개선수렴성병제고구해효솔。
Domain decomposition is one of the fundamental methods for parallel computing .During the solution of sparse linear systems with iterations , for the effective preconditioners in serial computation such as incomplete factorisation , it is usual to adopt the domain decomposition ideas to parallelise .But the essence of the domain decomposition is to approximate the global solution with local solutions , which must lead to significant errors .To reduce this error , a coarse grid correction algorithm is presented through the contraction of the non-overlapped sub-domains in this paper , with each sub-domain concentrating to a super node .A small linear system with small order is formed in this way, which contains the global information , and the order is equal to the number of domains .Then, the coarse grid operator is used to correct the original parallel preconditioners .Numerical experiments with block Jacobi-type, classical additive Schwarz , and factors combination-based parallel incomplete factorisation show that the provided coarse grid correction can improve the convergence effectively , thus improves the efficiency of the solution process .