Application of preconditioned block BiCGGR to the Wilson-Dirac equation with multiple right-hand sides in lattice QCD
نویسندگان
چکیده
There exist two major problems in application of the conventional block BiCGSTAB method to the O(a)-improved Wilson-Dirac equation with multiple right-hand-sides: One is the deviation between the true and the recursive residuals. The other is the convergence failure observed at smaller quark masses for enlarged number of the right-hand-sides. The block BiCGGR algorithm which was recently proposed by the authors succeeds in solving the former problem. In this article we show that a preconditioning technique allows us to improve the convergence behavior for increasing number of the right-hand-sides.
منابع مشابه
Application of block Krylov subspace algorithms to the Wilson-Dirac equation with multiple right-hand sides in lattice QCD
It is well known that the block Krylov subspace solvers work efficiently for some cases of the solution of differential equations with multiple right-hand sides. In lattice QCD calculation of physical quantities on a given configuration demands us to solve the Dirac equation with multiple sources. We show that a new block Krylov subspace algorithm recently proposed by the authors reduces the co...
متن کاملNew variants of the global Krylov type methods for linear systems with multiple right-hand sides arising in elliptic PDEs
In this paper, we present new variants of global bi-conjugate gradient (Gl-BiCG) and global bi-conjugate residual (Gl-BiCR) methods for solving nonsymmetric linear systems with multiple right-hand sides. These methods are based on global oblique projections of the initial residual onto a matrix Krylov subspace. It is shown that these new algorithms converge faster and more smoothly than the Gl-...
متن کاملDeflation of Eigenvalues for GMRES in Lattice QCD
This paper looks at the iterative solution of complex, non-Hermitian systems of linear equations associated with a lattice QCD problem in particle physics. Let the n by n system of equations be Ax = b. We use a version of the GMRES method that deflates eigenvalues and can solve systems with multiple right-hand sides. We give examples that show deflating eigenvalues can make a significant improv...
متن کاملSeed methods for linear equations in lattice qcd problems with multiple right-hand sides
We consider three improvements to seed methods for Hermitian linear systems with multiple right-hand sides: only the Krylov subspace for the first system is used for seeding subsequent right-hand sides, the first right-hand side is solved past convergence, and periodic reorthogonalization is used in order to control roundoff errors associated with the Conjugate Gradient algorithm. The method is...
متن کاملBlock Algorithms for Quark Propagator Calculation
Computing quark propagators in lattice QCD is equivalent to solving large, sparse linear systems with multiple right-hand sides. Block algorithms attempt to accelerate the convergence of iterative Krylov-subspace methods by solving the multiple systems simultaneously. This paper compares a block generalisation of the quasi-minimal residual method (QMR), Block Conjugate Gradient on the normal eq...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Computer Physics Communications
دوره 181 شماره
صفحات -
تاریخ انتشار 2010