A new way of modelling and solving partial differential equations is derived. While the finite element (FE) methodology is based on the integration over finite elements, this novel approach utilizes edges (finite lines) instead, which results in a finite line integration (FLIM). We present how the FE-computations over elements (areas or volumes) can be rewritten for the stiffness matrix based o...

Numerical simulation of ultrasonic wave propagation provides an efficient tool for crack identification in structures, while it requires a high resolution and expensive time calculation cost in both time integration and spatial discretization. Wavelet finite element model provides a highorder finite element model and gives a higher accuracy on spatial discretization, B-Spline wavelet interval (...

Scattering problems for periodic structures have been studied a lot in the past few years. A main idea for numerical solution methods is to reduce such problems to one periodicity cell. In contrast to periodic settings, scattering from locally perturbed periodic surfaces is way more challenging. In this paper, we introduce and analyze a new numerical method to simulate scattering from locally p...

We use a version of the FEM–BEM method introduced by Costabel [Boundary Elements IX, Vol. 1, C. A. Brebbia et al., eds., Springer-Verlag, 1987] and Han [J. Comput. Math., 8 (1990), pp. 223–232] to discretize an exterior quasilinear problem. We provide error estimates for the Galerkin method and propose a fully discrete scheme based on simple quadrature formulas. Furthermore, we show that these ...

The BEM is applied to the solution of the torsion problem of non-homogeneous anisotropic non-circular prismatic bars. The problem is formulated in terms of the warping function. This formulation leads to a second order partial differential equation with variable coefficients, subjected to a generalized Neumann type boundary condition. The problem is solved using the Analog Equation Method (AEM)...

It has been previously shown that the temporal integration of hyperbolic partial differential equations may , because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic p.d.e's (linear and non-linear) whose boundary treatment is done via t...

in this paper, we studied the numerical solution of nonlinear weakly singular volterra-fredholm integral equations by using the product integration method. also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear volterra-fredholm integral equations. the reliability and efficiency of the proposed scheme are...

We have developed a structured adaptive mesh refinement (SAMR) method for parabolic partial differential equation (PDE) systems. Solutions are calculated using the finite-difference or finite-volume method in space and backward differentiation formula (BDF) integration in time. The combination of SAMR in space and BDF in time is designed for problems where the fine-scale profile of sharp fronts...

Abstract. In this study, we consider new finite difference schemes for solving the Helmholtz equation. Novel difference schemes which do not introduce truncation error are presented, consequently the exact solution for the Helmholtz equation can be computed numerically. The most important features of the new schemes are that while the resulting linear system has the same simple structure as tho...