This article discusses the approach of developing MuPAD into an open and parallel problem solving environment for mathematical applications. It introduces the key technologies domains and dynamic modules and describes the current state of macroparallelism which covers three fields of parallel...

The adaptive BDDC method is extended to the selection of face constraints in three dimensions. A new implementation of the BDDC method is presented based on a global formulation without an explicit coarse problem, with massive parallelism provided by a multifrontal solver. Constraints are...

A parallel implementation of the Balancing Domain Decomposition based on Constraints (BDDC) method using the frontal solver is employed to solve systems of linear equations from finite element analysis, and incorporated into a standard finite element system for engineering analysis by linear...

In most recent substructuring methods, a fundamental role is played by the coarse space. For some of these methods (e.g. BDDC and FETI-DP), its definition relies on a ‘minimal’ set of coarse nodes (sometimes called corners) which assures invertibility of local subdomain problems and also of...

Three Monte Carlo methods for matrix inversion (MI) and finding a solution vector of a system of linear algebraic equations (SLAE) are considered: with absorption, without absorption with uniform transition frequency function, and without absorption with almost optimal transition frequency...

The numerical solution of 3D linear elasticity equations is considered. The problem is described by a coupled system of second-order elliptic partial differential equations. This system is discretized by trilinear parallelepipedal finite elements.

The numerical solution of 3D linear elasticity equations is considered. The problem is described by a coupled system of second-order elliptic partial differential equations. This system is discretized by trilinear brick finite elements. The PCG iterative method is used for solving the...

In many real-life applications of optimal control problems with constraints in form of partial differential equations (PDEs), hyperbolic equations are involved which typically describe transport processes. Since hyperbolic equations usually propagate discontinuities of initial or boundary...

The present paper deals with the application of the feedforward neural network in feedback control for dynamic systems. First, the problem of non-linear control is solved using the optimal control approach. Then assuming that prior knowledge is available in a certain form (input/output data-base...

This paper describes the functionality and implementation of COOPT. This software package implements a direct method with modified multiple shooting type techniques for solving optimal control problems of large-scale differential–algebraic equation (DAE) systems. The basic approach in COOPT is...