Two popular non-overlapping domain decomposition methods, the FETI–DP and BDDC algorithms, are reformulated using Block Cholesky factorizations, an approach which can provide a useful framework for the design of domain decomposition algorithms for solving symmetric positive definite linear system of equations. Instead of introducing Lagrange multipliers to enforce the coarse level, primal conti...

School of Basic Science Mathematics Section Master in Mathematical Engineering FETI-DP Domain Decomposition Method by Christoph Jäggli FETI-DP is a dual iterative, nonoverlapping domain decomposition method. By a Schur complement procedure, the solution of a boundary value problem is reduced to solving a symmetric and positive definite dual problem in which the variables are directly related to...

In this paper we investigate the construction of dyadic affine (wavelet) bi-frames for triangular-mesh surface multiresolution processing. We introduce 6-fold symmetric bi-frames with 4 framelets (frame generators). 6-fold symmetric bi-frames yield frame decomposition and reconstruction algorithms (for regular vertices) with high symmetry, which is required for the design of the corresponding f...

Global Krylov subspace methods are the most efficient and robust methods to solve generalized coupled Sylvester matrix equation. In this paper, we propose the nested splitting conjugate gradient process for solving this equation. This method has inner and outer iterations, which employs the generalized conjugate gradient method as an inner iteration to approximate each outer iterate, while each...

We consider the numerical solution of 3D linear elasticity equations. The investigated problem is described by a coupled system of second order elliptic partial differential equations. This system is then discretized by conforming or nonconforming finite elements. After applying the Finite Element Method (FEM) based discretization, a system of linear algebraic equations has to be solved. In thi...

For little q-Jacobi polynomials, q-Hahn polynomials and big q-Jacobi polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as decompositions into a lower triangular matrix times upper triangular matrix. We develop a general theory of such decompositions rela...