The paper discusses the effort carried out at VNIIEF to consider the applicability of unstructured Lagrange meshes to multidimensional continuum mechanics problems with high shear strain and vortex flows. Three finite-difference numerical techniques for solving continuum mechanics problems on polyhedral unstructured Lagrange meshes are described. Examples of numerical calculations of benchmark ...

facing the issues with structural complexity about which stakeholders have different views, has increasingly led to the use of soft systems methodology (ssm) in solving managerial problems. moreover, the flaws of this methodology in the stages of modeling and feasible, desirable changes, have provided the motivation for applying cognitive map (cm) and system dynamics in the ssm modeling. presen...

Multigrid has been a popular solver method for nite element and nite di erence problems with regular grids for over 20 years. The application of multigrid to unstructured problems is, however, not well understood and has been an active area of research in recent years. The two most promising categories of unstructured multigrid methods are 1) \geometric" methods that use standard nite element c...

The theory and application of numerical methods for unstructured meshes have been improved significantly in recent years. Because the grids can be place arbitrarily in space, unstructured meshes can provide much higher spatial resolution than regular meshes. The built-in nature of mesh adaptivity for unstructured meshes gives one way to simulate highly dynamic, hierarchical problems involving b...

We study optimal control problems for general unstructured nonlinear differential-algebraic equations of arbitrary index. In particular, we derive necessary conditions in the case of linear-quadratic control problems and extend them to the general nonlinear case. We also present a Pontryagin maximum principle for general unstructured nonlinear DAEs in the case of restricted controls. Moreover, ...

Unstructured parallelism is the hardest problem to analyze and to program. In this paper we present a generic approach TGEX for analyzing and executing unstructured problems. It separates the speciication of a computational problem from the control of the parallel execution. A computational problem is rst partitioned in terms of a computation task graph which serves as a machine-independent rep...

Unstructured parallelism is the hardest problem to analyze and to program. In this paper we present a generic approach TGEX for analyzing and executing unstructured problems. It separates the speciication of a computational problem from the control of the parallel execution. A computational problem is rst partitioned in terms of a computation task graph which serves as a machine-independent rep...

A discontinuous Galerkin formulation that avoids the use of discrete quadrature formulas is described and applied to linear and nonlinear test problems in one and two space dimensions. This approach requires less computational time and storage than conventional implementations but preserves the compactness and robustness inherent to the discontinuous Galerkin method. Test problems include both ...