A fast incremental/iterative solution procedure that handles "snap-through"

SUMMARY We present an introduction to the spectral element method, which provides an innovative numerical approach to the calculation of synthetic seismograms in 3-D earth models. The method combines the £exibility of a ¢nite element method with the accuracy of a spectral method. One uses a weak formulation of the equations of motion, which are solved on a mesh of hexahedral elements that is adapted to the free surface and to the main internal discontinuities of the model. The wave¢eld on the elements is discretized using high-degree Lagrange interpolants, and integration over an element is accomplished based upon the Gauss^Lobatto^Legendre integration rule. This combination of discretization and integration results in a diagonal mass matrix, which greatly simpli¢es the algorithm. We illustrate the great potential of the method by comparing it to a discrete wavenumber/re£ectivity method for layer-cake models. Both body and surface waves are accurately represented, and the method can handle point force as well as moment tensor sources. For a model with very steep surface topography we successfully benchmark the method against an approximate boundary technique. For a homogeneous medium with strong attenuation we obtain excellent agreement with the analytical solution for a point force.

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Introduction to the spectral element method for three-dimensional seismic wave propagation

Basic error estimates for elliptic problems

Effective properties of composite materials with periodic microstructure : a computational approach

From the Publisher:
Introduction to Numerical Continuation Methods continues to be useful for researchers and graduate students in mathematics, sciences, engineering, economics, and business looking for an introduction to computational methods for solving a large variety of nonlinear systems of equations. A background in elementary analysis and linear algebra is adequate preparation for reading this book; some knowledge from a first course in numerical analysis may also be helpful.

/pdf/introduction-to-numerical-continuation-methods-ily9kpadk5.pdf

Introduction to Numerical Continuation Methods

Incremental displacement algorithms for nonlinear problems

Modélisation des structures par éléments finis

Simplifies the teaching of the finite element method. Topics covered include: the approximation of continuous functions over sub-domains in terms of nodal values; interpolation functions for classical elements in one, two, and three dimensions; fundamental element vectors and matrices and assembly techniques; numerical methods of integration; matrix Eigenvalue and Eigenvector problems; and Fortran programming techniques. Contains tables of formulas and constants for constructing codes.

G. Dhatt

Papers

Incremental displacement algorithms for nonlinear problems

Modélisation des structures par éléments finis

The finite element method displayed

A finite element model of estuarian and river flows with moving boundaries

Stress analysis of the human aortic valve