Hafiz Abdul Wajid

Dispersive and Dissipative Behavior of the Spectral Element Method

If the nodes for the spectral element method are chosen to be the Gauss-Legendre-Lobatto points and a Lagrange basis is used, then the resulting mass matrix is diagonal and the method is sometimes then described as the Gauss-point mass lumped finite element scheme. We study the dispersive behavior of the scheme in detail and provide both a qualitative description of the nature of the dispersive and dissipative behavior of the scheme along with precise quantitative statements of the accuracy in terms of the mesh-size and the order of the scheme. We prove that (a) the Gauss-point mass lumped scheme (i.e., spectral element method) tends to exhibit phase lag whereas the (consistent) finite element scheme tends to exhibit phase lead; (b) the absolute accuracy of the spectral element scheme is

Optimally Blended Spectral-Finite Element Scheme for Wave Propagation and NonStandard Reduced Integration

1/p

NUMERICAL MODELING OF CAPILLARY–GRAVITY WAVES USING THE PHASE FIELD METHOD

times better than that of the finite element scheme despite the use of numerical integration; (c) when the order

Explicit Discrete Dispersion Relations for the Acoustic Wave Equation in d-Dimensions Using Finite Element, Spectral Element and Optimally Blended Schemes

p

Optimized bolt tightening procedure for different tightening strategies—FEA study

, the mesh-size

An optimally blended finite-spectral element scheme with minimal dispersion for Maxwell equations

h

Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave Number

, and the frequency of the wave

Comparative Modal Analysis of Gasketed and Nongasketed Bolted Flanged Pipe Joints: FEA Approach

\omega

Application of monotonic adaptive kernel for optimization: A case study:

satisfy

OPTIMIZATION OF BOX TYPE GIRDER WITH AND WITHOUT INDUSTRIAL CONSTRAINTS

2p+1 \approx \omega h