A mathematical model allowing coupled hygro-thermo-mechanical analysis of spalling in concrete walls at high temperatures by means of the moving boundary problem is presented. A simplified mechanical approach to account for effects of thermal stresses and pore pressure build-up on spalling is incorporated into the model. The numerical algorithm based on finite element discretization in space an...

The paper deals with the Darboux problem for the equation Dxyz(x, y) = f(x, y, z(x,y)) where z(x,y) is a function defined by z(x,y)(t, s) = z(x + t, y + s), (t, s) ∈ [−a0, 0]× [−b0, 0]. We construct a general class of difference methods for this problem. We prove the existence and uniqueness of solutions to implicit functional difference equations by means of a comparison method; moreover we gi...

To solve the heat equation on parallel computers, a high-order finite difference domain decomposition algorithm is discussed. In this procedure, interface values between subdomains are calculated by the classical explicit scheme, while interior values of sub-domains are determined by the famous forth-order compact scheme. The stability and convergence for this domain decomposition algorithm are...

Parallel finite difference schemes with high-order accuracy and unconditional stability for solving parabolic equations are presented. The schemes are based on domain decomposition method, i.e., interface values between subdomains are computed by the explicit scheme; interior values are computed by the implicit scheme. The numerical stability and error are derived in the H norm in one dimension...

We consider a divergence-free non-dissipative fourth-order explicit staggered nite di erence scheme for the hyperbolic Maxwell's equations. Special one-sided di erence operators are derived in order to implement the scheme near metal boundaries and dielectric interfaces. Numerical results show the scheme is long-time stable, and is fourth-order convergent over complex domains that include diele...

In this paper, the formulation of a new group explicit method with a fourth order accuracy is described in solving the two dimensional Helmholtz equation. The formulation is based on the nine-point fourth order compact finite difference approximation formula. The complexity analysis of the developed scheme is also presented. Several numerical experiments were conducted to test the feasibility o...

ACKNOWLEDGEMENTS I would like to truly thank all of my committee members for their encouragement and guidance in the preparation of this thesis. I especially want to express my gratitude to Dr. Kevin Clarno for his insight and assistance. My advisor, Dr. Cassiano de Oliveira, has been immensely helpful with his continuous encouragement and unique perspectives. Perhaps most of all, I want to tha...

Weighted automata can be seen as a natural generalization of finite state automata to more complex algebraic structures. The standard reasoning tasks for unweighted automata can also be generalized to the weighted setting. In this report we study the problems of intersection, complementation, and inclusion for weighted automata on infinite trees and show that they are not harder complexity-wise...

In this study, the finite difference method is applied to an optimal control problem controlled by two functions which are in the coefficients of two-dimensional Schrodinger equation. Convergence of the finite difference approximation according to the functional is proved. We have used the implicit method for solving the two-dimensional Schrodinger equation. Although the implicit scheme obtaine...

Simulation of dynamic motion of soft tissues is one of the most important topic in nowadays computer animation of human body. So far various elastically deformable models were used for this purpose. We present the extension of model proposed in [15] with volume preserving constraint. We provide also evaluation of the constraint accuracy on two simulation experiments. Furthermore we add model of...