Background
The aim of electroencephalogram (EEG) source localization is to find the brain areas responsible for EEG waves of interest. It consists of solving forward and inverse problems. The forward problem is solved by starting from a given electrical source and calculating the potentials at the electrodes. These evaluations are necessary to solve the inverse problem which is defined as finding brain sources which are responsible for the measured potentials at the EEG electrodes.

/pdf/review-on-solving-the-forward-problem-in-eeg-source-analysis-4susg04pdg.pdf

Review on solving the forward problem in EEG source analysis

We present a review of the recent development in finite-difference time-domain modeling of seismic wave propagation and earthquake motion. The finite-difference method is a robust numerical method applicable to structurally complex media. Due to its relative accuracy and computational efficiency it is the dominant method in modeling earthquake motion and it also is becoming increasingly more important in the seismic industry and for structural modeling. We first introduce basic formulations and properties of the finite-difference schemes including promising recent advances. Then we address important topics as material discontinuities, realistic attenuation, anisotropy, the planar free surface boundary condition, free-surface topography, wavefield excitation (including earthquake source dynamics), non-reflecting boundaries, and memory optimization and parallelization.

The finite-difference time-domain method for modeling of seismic wave propagation

https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1105&context=mechengfacpub

A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities

FE-formulation of a nonlocal plasticity theory

Within the well-known and highly effective finite element method for the computation of approximate solutions of complex boundary value problems, we focus on the often-called mixed finite element methods, where in our terminology the word ‘mixed’ indicates the fact that the problem discretization typically results in a linear algebraic system characterized by a null matrix on the main diagonal.



Accordingly, the goals of the present chapter are: (1) to sketch out that several physical problems share such an algebraic structure once a discretization is introduced; (2) to present a simple, algebraic version of the abstract theory that rules most applications of mixed finite element methods; (3) to give several examples of efficient mixed finite element methods; (4) finally, to give some hints on how to perform a stability and error analysis, focusing on a representative problem.


Keywords:

mixed finite elements;
potential energy;
Hellinger-Reissner;
Hu-Washizu;
thermal diffusion;
stokes;
nearly incompressible elasticity;
stability conditions

/pdf/mixed-finite-element-methods-41ej5stuus.pdf

Mixed Finite Element Methods

* Introduction. * Matrix Algebra. * Direct Approach. * Strong and Weak Formulations - One-dimensional Heat Flow. * Gradient - Gauss' Divergence Theorem - Green Theorem. * Strong and Weak Forms - Two-and Three-Dimensional Heat Flow. * Choice of Approximating Functions for the FE-method - Scalar Problems. * Choice of Weight Function - Weighted Residual Methods. * FE-formulation of One-Dimensional Heat Flow. * FE-formulation of Two-and-Three Dimensional Heat Flow. * Guidelines for Element Meshes and Global Nodal Numbering. * Stresses and Strains. * Linear Elasticity. * FE-formulation of Torsion and Non-circular Shafts. * Approximating Functions for the FE-method - Vector Problems. * FE-formulation of Three-and-Two Dimensional Elasticity. * FE-formulation of Beams. * FE-formulation of Plates. * Isoparametric Finite Elements. * Numerical Integration.

/pdf/introduction-to-the-finite-element-method-28u1x13eld.pdf

Niels Saabye Ottosen

Papers

Introduction to the finite element method