A stable hybrid method for hyperbolic problems that combines the unstructured finite volume method with high-order finite difference methods has been developed. The coupling procedure is based on energy estimates and stability can be guaranteed. Numerical calculations verify that the hybrid method is efficient and accurate.

An adaptive unstructured grid generation scheme is introduced to use finite volume (FV) and finite element (FE) formulation to solve the heat equation with singular boundary conditions. Regular grids could not acheive accurate solution to this problem. The grid generation scheme uses an optimal time complexity frontal method for the automatic generation and delaunay triangulation of the grid po...

In this paper, we introduce a simple method for the Cauchy problem. This new finite element method is based on least squares methodology with discontinuous approximations which can be implemented and analyzed easily. This discontinuous Galerkin finite element method is flexible to work with general unstructured meshes. Error estimates of the finite element solution are derived. The numerical ex...

We present the Discrete Duality Finite Volume method (DDFV) for solving the linear elasticity problem on unstructured mesh applied to solids undergoing mechanical loads. The procedure is described in detail for three dimensional problems and some theoretical results are provided: the discrete problem is well-posed, stable and convergent. A number of numerical test problems demonstrates the abil...

The design of a parallel implementation of multilevel recursive spectral bisection is described. The goal is to implement a code _ha_ is fast enough to enable dynamic repartitioning of adaptive meshes. 1 Background The R.ecursive Spectral Bisection (I_SB) _lgori_hm is one of a class of recursive bisection methods for partitioning unstructured problems [4]. RSB is typically used as a preprocessi...

This paper reviews and extends the theory and application of mimetic finite difference methods for the solution of diffusion problems in strongly heterogeneous anisotropic materials. These difference operators satisfy the fundamental identities, conservation laws and theorems of vector and tensor calculus on nonorthogonal, nonsmooth, structured and unstructured computational grids. We provide e...

We propose to construct MAPS, a collection-oriented SPMD programming environment for writing parallel programs that will simplify the development and porting of many scientific algorithms, both structured and unstructured. This very general class of applications includes finite-difference, finite-element and finite-volume methods, multiblock and multigrid algorithms, PIC codes for simulating pl...

The paper describes the implementation details and validation results for an agglomeration multigrid procedure developed in the context of hybrid, unstructured grid solutions of aerodynamic flows. The procedure is applied to the solution of 2-D, laminar viscous flows of aerospace interest. The governing equations are discretized with an unstructured grid finite volume method which is capable of...