Condition number study of graph theory based preconditioners for isogeometric discretization of Poisson equation
نویسندگان
چکیده
We study the preconditioning of the stiffness matrix which arises from the discretization of the Poisson equation using IsoGeometric Method (IGM). A study of condition number of stiffness matrices, resulting from NURBS based IGM, suggests that novel preconditioning techniques are needed for fast and efficient iterative solvers for the resulting linear system. As a first step towards preconditioning the resulting stiffness matrix, we use graph theory based preconditioners, namely, Vaidya’s preconditioners (maximum weight spanning tree) and Gremban and Miller’s preconditioners (support tree). Numerical results show that these preconditioners do not perform satisfactorily for the matrices arising in IGM.
منابع مشابه
Isogeometric Analysis: Condition Number Estimates and Fast Solvers
Isogeometric methods were introduced by Hughes et al. in 2005. Since its introduction these methods have been used in many practical problems in science and engineering. However, so far, only few papers appeared in the field of iterative solvers for these methods. This thesis contributes to the development of fast iterative solvers for the matrices arising in isogeometric discretization of elli...
متن کاملBounding the Influence of Domain Parameterization and Knot Spacing on Numerical Stability in Isogeometric Analysis
Isogeometric Analysis (IGA) was introduced by Hughes et al. in 2005 [1] as a new method to bridge the gap between the geometry description and numerical analysis. Similar to the finite element approach, the IGA concept to solve a partial differential equation leads to a (linear) system of equations. The condition number of the coefficient matrix is a crucial factor for the stability of the syst...
متن کاملUniform preconditioners for the time dependent Stokes problem
Implicit time stepping procedures for the time dependent Stokes problem lead to stationary singular perturbation problems at each time step. These singular perturbation problems are systems of saddle point type, which formally approach a mixed formulation of the Poisson equation as the time step tends to zero. Preconditioners for discrete analogous of these systems are discussed. The preconditi...
متن کاملMultilevel Preconditioners for Strongly Anisotropic Problems
In this dissertation, we develop new multilevel approaches to precondition algebraic problems stemming from the finite volume discretization of the diffusion equation with anisotropic, discontinuous coefficients. Two approaches are discussed. In the first approach, preconditioners are based on a partitioning of the mesh in the (x, y)-plane into non-overlapping subdomains and on a special coarse...
متن کاملAdaptive Selection of Primal Constraints for Isogeometric BDDC Deluxe Preconditioners
Isogeometric analysis has been introduced as an alternative to finite element methods in order to simplify the integration of CAD software and the discretization of variational problems of continuum mechanics. In contrast with the finite element case, the basis functions of isogeometric analysis are often not nodal. As a consequence, there are fat interfaces which can easily lead to an increase...
متن کامل