Two Preconditioners for Time-Harmonic Eddy-Current Optimal Control Problems

被引：0

作者：

Shao, Xin-Hui ^{[1
]}

Dong, Jian-Rong ^{[1
]}

机构：

[1] Northeastern Univ, Coll Sci, Dept Math, Shenyang 100098, Peoples R China

来源：

MATHEMATICS | 2024年 / 12卷 / 03期

关键词：

PDE-constrained optimization; Krylov subspace methods; eddy currents; preconditioner; MIXED FINITE-ELEMENTS; ITERATION METHODS; SCHUR COMPLEMENT; SYSTEMS;

D O I：

10.3390/math12030375

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the numerical solution of a large complex linear system with a saddle-point form obtained by the discretization of the time-harmonic eddy-current optimal control problem. A new Schur complement is proposed for this algebraic system, extending it to both the block-triangular preconditioner and the structured preconditioner. A theoretical analysis proves that the eigenvalues of block-triangular and structured preconditioned matrices are located in the interval [1/2, 1]. Numerical simulations show that two new preconditioners coupled with a Krylov subspace acceleration have good feasibility and effectiveness and are superior to some existing efficient algorithms.

引用

页数：17

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