A tree-based dataflow model for the unsymmetric multifrontal method.
A triangular mixed finite element method for the stationary semiconductor device equations
A tribute to Bernard Bolzano
A truncated descent HS conjugate gradient method and its global convergence.
A trust-region-based BFGS method with line search technique for symmetric nonlinear equations.
A twisted block tangential filtering decomposition preconditioner.
A two parameter iterative method for solving algebraic systems of domain decomposition type
An iterative procedure containing two parameters for linear algebraic systems originating from the domain decomposition technique is proposed. The optimization of the parameters is investigated. A numeric example is given as an illustration.
A Two Point Boundary Value Problem with a Rapidly Oscillating Solution.
A two-dimensional inverse heat conduction problem for estimating heat source.
A two-fluid hyperbolic model in a porous medium
The paper is devoted to the computation of two-phase flows in a porous medium when applying the two-fluid approach. The basic formulation is presented first, together with the main properties of the model. A few basic analytic solutions are then provided, some of them corresponding to solutions of the one-dimensional Riemann problem. Three distinct Finite-Volume schemes are then introduced. The first two schemes, which rely on the Rusanov scheme, are shown to give wrong approximations in some...
A two-level discretization method for the stationary MHD equations.
A two-stage Newton-like method for computing simple bifurcation points of nonlinear equations depending on two parameters
A unified analysis of elliptic problems with various boundary conditions and their approximation
We design an abstract setting for the approximation in Banach spaces of operators acting in duality. A typical example are the gradient and divergence operators in Lebesgue-Sobolev spaces on a bounded domain. We apply this abstract setting to the numerical approximation of Leray-Lions type problems, which include in particular linear diffusion. The main interest of the abstract setting is to provide a unified convergence analysis that simultaneously covers (i) all usual boundary conditions, (ii)...
A Unified Approach for Constructing Fast Two-Step Newton-like Methods.
A unified approach to a posteriori error estimation using element residual methods.
A Unified Approach to Methods for the Simultaneous Computation of All Zeros of Generalized Polynomials.
A unified approach to singular problems arising in the membrane theory
We consider the singular boundary value problem where is a given continuous function defined on the set which can have a time singularity at and a space singularity at . Moreover, , , and , , are real constants such that , whereas . The main aim of this paper is to discuss the existence of solutions to the above problem and apply the general results to cover certain classes of singular problems arising in the theory of shallow membrane caps, where we are especially interested in...
A unified approach to some strategies for the treatment of breakdown in Lanczos-type algorithms
The Lanczos method for solving systems of linear equations is implemented by using some recurrence relationships between polynomials of a family of formal orthogonal polynomials or between those of two adjacent families of formal orthogonal polynomials. A division by zero can occur in these relations, thus producing a breakdown in the algorithm which has to be stopped. In this paper, three strategies to avoid this drawback are discussed: the MRZ and its variants, the normalized and unnormalized...
A unified convergence analysis for local projection stabilisations applied to the Oseen problem
The discretisation of the Oseen problem by finite element methods may suffer in general from two shortcomings. First, the discrete inf-sup (Babuška-Brezzi) condition can be violated. Second, spurious oscillations occur due to the dominating convection. One way to overcome both difficulties is the use of local projection techniques. Studying the local projection method in an abstract setting, we show that the fulfilment of a local inf-sup condition between approximation and projection spaces...
A unified convergence theory for and algorithms applied to symmetric eigenvalue problems
In this paper we consider the eigenvalue problem for positive definite symmetric matrices. Convergence properties for the zero shift method and the shift Cholesky method both in restoring and in non restoring version are deduced from the convergence properties of triangular matrices sequences. For general matrices we obtain some results on the convergence speed of the Cholesky method as a function of the chosen shift. These results follow from the absolute convergence of numerical series associated...