We introduce some multilevel and multigrid methods and derive their global convergence rate for variational inequalities and for variational inequalities containing a term introduced by a nonlinear operator. Also, we ...
详细信息
The spread of electrical excitation in the cardiac muscle and the subsequent contraction-relaxation process is quantitatively described by the cardiac electromechanical coupling model. The electrical model consists of...
详细信息
In this paper we introduce an Average Additive Schwarz method with spectrally enriched coarse grids for a standard Finite Element discretization of a second order elliptic problem with discontinuous coefficients, wher...
详细信息
We consider two recently developed adaptive grid methods for solving time dependent partial differential equations (PDEs) in higher dimensions. These methods compute the adaptive grid based on solving an optimal mass ...
详细信息
ISBN:
(数字)9783319672021
ISBN:
(纸本)9783319672021;9783319672014
We consider two recently developed adaptive grid methods for solving time dependent partial differential equations (PDEs) in higher dimensions. These methods compute the adaptive grid based on solving an optimal mass transport problem also known as Monge-Kantorovich problem (MKP). The optimal solution of the MKP is reduced to solving Monge-Ampere equation and is known to have some nice theoretical properties that are desirable for the mesh adaptation. However, these two adaptive grid methods solve the Monge-Ampere equation differently and they are distinctly different in their approaches for computing the adaptive mesh over time. A comparison study to address these various distinctions between the two methods is presented. Several numerical experiments are conducted to illustrate the main differences between the two methods in terms of their mesh quality and performances.
The idea of preconditioning iterative methods for the solution of linear systems goes back to Jacobi (Astron Nachr 22(20):297-306, 1845), who used rotations to obtain a system with more diagonal dominance, before he a...
详细信息
In this paper, we study the adaptive selection of primal constraints in BDDC deluxe preconditioners applied to isogeometric discretizations of scalar elliptic problems. The main objective of this work is to significan...
详细信息
For a specially structured nonsymmetric banded matrix, which is related to a discrete integrable system, we propose a novel method to compute all the eigenvectors. We show that the eigenvector entries are arranged rad...
详细信息
ISBN:
(数字)9783319624266
ISBN:
(纸本)9783319624266;9783319624242
For a specially structured nonsymmetric banded matrix, which is related to a discrete integrable system, we propose a novel method to compute all the eigenvectors. We show that the eigenvector entries are arranged radiating out from the origin on the complex plane. This property enables us to efficiently compute all the eigenvectors. Although the intended matrix has complex eigenvalues, the proposed method can compute all the complex eigenvectors using only arithmetic of real numbers.
The ILU factorization is one of the most popular preconditioners for the Krylov subspace method, alongside the GMRES. Properties of the preconditioner derived from the ILU factorization are relayed onto the dropping r...
详细信息
ISBN:
(数字)9783319624266
ISBN:
(纸本)9783319624266;9783319624242
The ILU factorization is one of the most popular preconditioners for the Krylov subspace method, alongside the GMRES. Properties of the preconditioner derived from the ILU factorization are relayed onto the dropping rules. Recently, Zhang et al. (Numer Linear Algebra Appl 19:555-569, 2011) proposed a Flexible incomplete Cholesky (IC) factorization for symmetric linear systems. This paper is a study of the extension of the IC factorization to the nonsymmetric case. The new algorithm is called the Crout version of the flexible ILU factorization, and attempts to reduce the number of nonzero elements in the preconditioner and computation time during the GMRES iterations. Numerical results show that our approach is effective and useful.
We have developed a computer code to find eigenvalues and eigenvectors of non-Hermitian sparse matrices arising in lattice quantum chromodynamics (lattice QCD). The Sakurai-Sugiura (SS) method (Sakurai and Sugiura, J ...
详细信息
ISBN:
(纸本)9783319624266;9783319624242
We have developed a computer code to find eigenvalues and eigenvectors of non-Hermitian sparse matrices arising in lattice quantum chromodynamics (lattice QCD). The Sakurai-Sugiura (SS) method (Sakurai and Sugiura, J Comput Appl Math 159:119, 2003) is employed here, which is based on a contour integral, allowing us to obtain desired eigenvalues located inside a given contour of the complex plane. We apply the method here to calculating several low-lying eigenvalues of the non-Hermitian O(a)-improved Wilson-Dirac operator D (Sakurai et al., Comput Phys Commun 181:113, 2010). Evaluation of the low-lying eigenvalues is crucial since they determine the sign of its determinant detD, important quantity in lattice QCD. We are particularly interested in such cases as finding the lowest eigenvalues to be equal or close to zero in the complex plane. Our implementation is tested for the Wilson-Dirac operator in free case, for which the eigenvalues are analytically known. We also carry out several numerical experiments using different sets of gauge field configurations obtained in quenched approximation as well as in full QCD simulation almost at the physical point. Various lattice sizes LxLyLzLt are considered from 8(3) x 16 to 96(4), amounting to the matrix order 12L(x)L(y)L(z)L(t) from 98,304 to 1,019,215,872.
In the present paper, we propose an extension of the Sakurai-Sugiura projection method (SSPM) for a circumference region on the complex plane. The SSPM finds eigenvalues in a specified region on the complex plane and ...
详细信息
ISBN:
(数字)9783319624266
ISBN:
(纸本)9783319624266;9783319624242
In the present paper, we propose an extension of the Sakurai-Sugiura projection method (SSPM) for a circumference region on the complex plane. The SSPM finds eigenvalues in a specified region on the complex plane and the corresponding eigenvectors by using numerical quadrature. The original SSPM has also been extended to compute the eigenpairs near the circumference of a circle on the complex plane. However these extensions can result in division by zero, if the eigenvalues are located at the quadrature points set on the circumference. Here, we propose a new extension of the SSPM, in order to avoid a decrease in the computational accuracy of the eigenpairs resulting from locating the quadrature points near the eigenvalues. We implement the proposed method in the SLEPc library, and examine its performance on a supercomputer cluster with many-core architecture.
暂无评论