How to avoid the use of Green's theorem in the Ciarlet-Raviart theory of variational crimes
How to Get around a Simple Quadratic Fold.
How to increase convergence order of the Newton method to ?
We present a simple and effective scheme for forming iterative methods of various convergence orders. In this scheme, methods of various convergence orders, such as four, six, eight and ten, are formed through a modest modification of the classical Newton method. Since the scheme considered is a simple modification of the Newton method, it can be easily implemented in existing software packages, which is also suggested by the presented pseudocodes. Finally some problems are solved, to very high...
How to Increase the Order to Get Minimal-Error Algorithms for Systems of ODE.
How to recover the gradient of linear elements on nonuniform triangulations
We propose and examine a simple averaging formula for the gradient of linear finite elements in whose interpolation order in the -norm is for and nonuniform triangulations. For elliptic problems in we derive an interior superconvergence for the averaged gradient over quasiuniform triangulations. A numerical example is presented.
hp-FEM for three-dimensional elastic plates
In this work, we analyze hierarchic hp-finite element discretizations of the full, three-dimensional plate problem. Based on two-scale asymptotic expansion of the three-dimensional solution, we give specific mesh design principles for the hp-FEM which allow to resolve the three-dimensional boundary layer profiles at robust, exponential rate. We prove that, as the plate half-thickness ε tends to zero, the hp-discretization is consistent with the three-dimensional solution to any power of ε in...
HP-finite element approximations on non-matching grids for partial differential equations with non-negative characteristic form
We propose and analyze a domain decomposition method on non-matching grids for partial differential equations with non-negative characteristic form. No weak or strong continuity of the finite element functions, their normal derivatives, or linear combinations of the two is imposed across the boundaries of the subdomains. Instead, we employ suitable bilinear forms defined on the common interfaces, typical of discontinuous Galerkin approximations. We prove an error bound which is optimal with respect...
H-Splittings and two-stage iterative methods.
Hybrid Algorithm for Fast Toeplitz Orthogonalization.
Hybrid central-upwind schemes for numerical resolution of two-phase flows
In this paper we present a methodology for constructing accurate and efficient hybrid central-upwind (HCU) type schemes for the numerical resolution of a two-fluid model commonly used by the nuclear and petroleum industry. Particularly, we propose a method which does not make use of any information about the eigenstructure of the jacobian matrix of the model. The two-fluid model possesses a highly nonlinear pressure law. From the mass conservation equations we develop an evolution equation which...
Hybrid central-upwind schemes for numerical resolution of two-phase flows
In this paper we present a methodology for constructing accurate and efficient hybrid central-upwind (HCU) type schemes for the numerical resolution of a two-fluid model commonly used by the nuclear and petroleum industry. Particularly, we propose a method which does not make use of any information about the eigenstructure of the Jacobian matrix of the model. The two-fluid model possesses a highly nonlinear pressure law. From the mass conservation equations we develop an evolution equation which...
Hybrid GA-SQP algorithms for three-dimensional boundary detection problems in potential corrosion damage.
Hybrid model for the Coupling of an Asymptotic Preserving scheme with the Asymptotic Limit model: The One Dimensional Case⋆
In this paper a strategy is investigated for the spatial coupling of an asymptotic preserving scheme with the asymptotic limit model, associated to a singularly perturbed, highly anisotropic, elliptic problem. This coupling strategy appears to be very advantageous as compared with the numerical discretization of the initial singular perturbation model or the purely asymptotic preserving scheme introduced in previous works [3, 5]. The model problem addressed...
Hybrid parallelization of an adaptive finite element code
We present a hybrid OpenMP/MPI parallelization of the finite element method that is suitable to make use of modern high performance computers. These are usually built from a large bulk of multi-core systems connected by a fast network. Our parallelization method is based firstly on domain decomposition to divide the large problem into small chunks. Each of them is then solved on a multi-core system using parallel assembling, solution and error estimation. To make domain decomposition for both, the...
Hybrid variational principles and their use in the finite element method
Hyperbolic relaxation models for granular flows
In this work we describe an efficient model for the simulation of a two-phase flow made of a gas and a granular solid. The starting point is the two-velocity two-pressure model of Baer and Nunziato [Int. J. Multiph. Flow16 (1986) 861–889]. The model is supplemented by a relaxation source term in order to take into account the pressure equilibrium between the two phases and the granular stress in the solid phase. We show that the relaxation process can be made thermodynamically coherent with an...
Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation
In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed....
Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation
In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed. Elements of a discretization of the eigenvalue...
Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation
In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed. Elements of a discretization of the eigenvalue...
Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation
In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed....