The Material Point Method (MPM) discrete solution procedure for computational solid mechanics is generalized using a variational form and a Petrov– Galerkin discretization scheme, resulting in a family of methods named the Generalized Interpolation Material Point (GIMP) methods. The generalization permits identification with aspects of other point or node based discrete solution techniques whic...

We propose a new approach for the simulation of conjugate heat exchangers. First, we introduce a dimensionality-reduced mathematical model for conjugate (fluid-solid) heat transfer: in the fluid channels, we consider a mixed-mean temperature defined on one-dimensional filaments; in the solid we consider a detailed partial differential equation conduction representation. We then propose a Petrov...

The use of " ideal " optimal test functions in a Petrov-Galerkin scheme guarantees the discrete stability of the variational problem. However, in practice, the computation of the ideal optimal test functions is computationally intractable. In this paper, we study the effect of using approximate, " practical " test functions on the stability of the DPG (discontinuous Petrov-Galerkin) method and ...

This paper is concerned with the stability of Petrov-Galerkin discretizations with application to parabolic evolution problems in space-time weak form. We will prove that the discrete inf-sup condition for an a priori fixed Petrov-Galerkin discretization is satisfied uniformly under standard approximation and smoothness conditions without any further coupling between the discrete trialand test ...

A nonlinear formulation of the Meshless Local Petrov-Galerkin (MLPG) finite-volume mixed method is developed for the large deformation analysis of static and dynamic problems. In the present MLPG large deformation formulation, the velocity gradients are interpolated independently, to avoid the time consuming differentiations of the shape functions at all integration points. The nodal values of ...

In this paper we formulate and analyze a Discontinuous Petrov Galerkin formulation of linear transport equations with variable convection fields. We show that a corresponding infinite dimensional mesh-dependent variational formulation, in which besides the principal field also its trace on the mesh skeleton is an unknown, is uniformly stable with respect to the mesh, where the test space is a c...

We develop a unified Petrov-Galerkin spectral method for a class of fractional partial differential equations with two-sided derivatives and constant coefficients of the form 0 D t u+ ∑d i=1 [cli aiD 2μi xi u+cri xiD 2μi bi u]+γ u = ∑d j=1 [κl j a jD 2ν j x j u+κr j x jD 2ν j b j u]+ f , where 2τ ∈ (0, 2), 2μi ∈ (0, 1) and 2ν j ∈ (1, 2), in a (1+d)-dimensional space-time hypercube, d = 1, 2, 3,...

Herein, we build and implement a combination of Lucas polynomials basis that fulfills the spatial homogenous boundary conditions. This is then used to solve time-fractional diffusion equation spectrally. The elements all spectral matrices are explicitly obtained in terms Gauss hypergeometric function. convergence error analysis proposed expansion studied. Numerical results indicate high accurac...

A meshless method based on the local Petrov-Galerkin approach is proposed, to solve boundary and initial value problems of piezoelectric and magnetoelectric-elastic solids with continuously varying material properties. Stationary and transient dynamic 2-D problems are considered in this paper. The mechanical fields are described by the equations of motion with an inertial term. To eliminate the...