This paper is devoted to the simulation of water forced evaporation in a porous saturated medium in a 3Daxisymmetric domain by resolution of partial differential algebraic equations (PDAE) that are encountered in different engineering applications. The goal of this paper is an attempt to present effective realizations, in order to determine the minimal duration of burning for prehistoric occupa...

In this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. The sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations to the nonlinear algebraic equations. Then, the Newton-Raphson method is used for solving these sets of algebraic equations. To present ability ...

2-D convection-diffusion, reacting flows in a single channel of catalytic monoliths are investigated. The fluid dynamics are modelled by a steady state, boundary-layer equations, which is a large system of parabolic partial differential equations (PDEs) with nonlinear boundary conditions arising from the coupling between the gas-phase and surface processes. The chemical processes are modelled u...

In the simulation of flows, the correct treatment of the pressure variable is the key to stable time-integration schemes. This paper contributes a new approach based on the theory of differential-algebraic equations. Motivated by the index reduction technique of minimal extension, a decomposition of finite element spaces is proposed that ensures stable and accurate approximations. The presented...

A mixed polynomial matrix is a polynomial matrix which has two kinds of nonzero coefficients: fixed constants that account for conservation laws and independent parameters that represent physical characteristics. This paper presents an algorithm for computing the degrees of all cofactors simultaneously in a regular mixed polynomial matrix. The algorithm is based on the valuated matroid intersec...

We conduct simulations for the 3D unsteady state anisotropic diffusion process with DT-MRI data in the human brain by discretizing the governing diffusion equation on Cartesian grid and adopting a high performance differential–algebraic equation (DAE) solver, the parallel version of implicit differential–algebraic (IDA) solver, to tackle the resulting large scale system of DAEs. Parallel precon...

The present talks deals with a uniform approach to the discretization in time of rigid body dynamics, nonlinear structural mechanics and flexible multibody systems. In particular, it is shown that a uniform set of differential-algebraic equations (DAEs) with constant mass matrix governs the motion of rigid bodies and semi-discrete formulations of structural components (such as geometrically exa...

Systems of differential-algebraic equations (DAEs) are generated routinely by simulation and modeling environments such as MODELICA and MAPLESIM. Before a simulation starts and a numerical solution method is applied, some kind of structural analysis is performed to determine the structure and the index of a DAE. Structural analysis methods serve as a necessary preprocessing stage, and among the...

with x0 ∈ R, B ∈ R and E,A ∈ R, such that the pencil sE − A ∈ R[s] is regular, that is, det(sE −A) 6= 0. For systems governed by ordinary differentialequations (that is, E is the identity matrix), a rigorous analysis of this problem has its origin in the 60s of the 20th century [6, 8–10, 13, 15, 21]. In particular, the article [20] by Willems gives a complete characterization of linear-quadrati...

Systems of differential-algebraic equations (DAEs) are generated routinely by simulation and modeling environments, such as MapleSim and those based on the Modelica language. Before a simulation starts and a numerical method is applied, some kind of structural analysis is performed to determine which equations to be differentiated, and how many times. Both Pantelides’s algorithm and Pryce’s Σ -...