In this paper an efficient analytical method is presented for calculating the eigenvalues of special matrices related to finite element meshes (FEMs) with regular topologies. In the proposed method, a skeleton graph is used as the model of a FEM. This graph is then considered as the Cartesian product of its generators. The eigenvalues of the Laplacian matrix of the entire graph are then easily ...

Spectral partitioning methods use the Fiedler vector—the eigenvector of the second-smallest eigenvalue of the Laplacian matrix—to find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to work extremely well. In this paper, we show that spectral partitioning methods work well on bounded-degree pl...

The Computational Singular Perturbation (CSP) method, developed by Lam and Goussis [Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988, pp. 931–941], is a commonly-used method for finding approximations of slow manifolds in systems of ordinary differential equations (ODEs) with multiple time scales. The validity of the CSP method was established fo...

This minisymposium focuses on recent advances on efficient and accurate numerical methods for PDEs and their various applications in physical or biological systems. The invited researchers will discuss a wide range of computational methods ranging from efficient finite element and finite difference methods, adaptive methods, multiscale methods, to spectral methods and kinetic Monte Carlo simula...

Differential equations have several applications in several fields such as: physics, fluid dynamic and geophysics etc. However it is not always possible to get the solution in closed form and thus, numerical methods come into the picture. There are several numerical methods to handle a variety of problems: Finite Difference Method, Spectral Method, Finite Element Method, Finite Volume Method an...

modelling of crack propagation by finite element method under mixed mode conditions is of prime importance in fracture mechanics. this paper describes an application of finite element method to the analysis of mixed mode crack growth in linear elastic fracture mechanics. crack growth process is simulated by an incremental crack-extension analysis based on the maximum principal stress criterion,...

This work investigates two physics-based models that simulate the non-linear partial differential algebraic equations describing an electric double layer supercapacitor. In one model the linear dependence between electrolyte concentration and conductivity is accounted for, while in the other model it is not. A spectral element method is used to discretise the model equations and it is found tha...

in this study, a new method for joining aluminum tubes in subsurface structures using steel converting and aluminum welding are presented and reviewed. but near the weld area is under high thermal cycle and will cause residual stresses in heat affected zone. therefore for assessment of proposed connection from the perspective of residual stress by using the finite element method welding of tube...

the complete 3d nonlinear dynamic problem of extensible, flexible risers conveying fluid is considered. for describing the dynamics of the system, the newtonian derivation procedure is followed. the velocity field inside the pipe formulated using hydrostatic and bernoulli equations. the hydrodynamic effects of external fluids are taken into consideration through the nonlinear drag forces in var...