"Methods of Computer Modeling in Engineering & the Sciences" (Satya N. Atluri)

OBJECTIVE: eat up

collection of recent paper and especially on mixed method

Part I Weak Forms, Weighted Residuals, Collocation, Subdomain, Finite Volume, Finite Element, Field/Boundary Element,
Meshless Local Petrov-Galerkin, and Boundary Methods, for Linear& Nonlinear Problems
I Introduction; II A Thin Beam on an Elastic Foundation; III Collocation, Subdomain, & Finite Volume Methods: §3.1 Point Collocation Method; §3.2
Weighted Integral Square Error Method; §3.3 Subdomain Integral/Average Error Method; §3.4 The Finite Volume Method; IV The Weighted Residual Method; V Local Element-wise Basis Functions: The Galerkin Finite Element Method Based on a Symmetric weak-Form; VI Numerical Quadrature;
§6.1 Numerical Quadrature; VII Details of Implementation of the Galerkin Finite Element Method; §7.1 An Algorithm for the Assembly of the Global
Stiffness Matrix in FEM; §7.2 Boundary Conditions; §7.3 Linear Equation Solver; VIII Shear Flexible Beam; Locking in Galerkin FEM; & Locking
Free Formulations; IX Primal & Mixed Galerkin Finite Element Formulations for a Realistic Beam on an Elastic Foundation; §9.1 Segmental formula-
tion of FEM for a Realistic Beam; §9.2 Single Field or Primitive Variable Symmetric Variational Form; §9.3 Multi-fi eld or Mixed Variable Symmetric
Variational Finite Element Method; §9.4 Mixed Method; Limitation Principle; Degenerating to Single-Field Method; §9.5 Complementary Energy
Approach; §9.6 Mixed/Hybrid Methods in Solid Mechanics: X Unsymmetric Weak Forms; Field/Boundary Integral Equations; & The Field/Boundary
Element Method; XI Meshless Trial & Test Functions & The Primal & Mixed Meshless Local Petrov- Galerkin (MLPG) Methods; §11.1 Introduction;
§11.2 Meshless Interpolation of the Trial Function: the MLS Method; §11.2.1 Accuracy of the MLS Interpolation; §11.2.2 Generalized moving least
squares interpolation; §11.3 Local Weak Forms and the Primal & Mixed MLPG Methods; §11.3.1 The Unsymmetric Weak Form 1; §11.3.2 Unsymmetric
local weak form 2; §11.3.3 Symmetric local weak form 3; §11.3.4 Unsymmetric local weak form 4; §11.3.5 Unsymmetric local weak form 5; §11.4 The
MLPG Mixed Methods ; §11.4.1 Mixed MLPG Method Based on Independent Interpolations; §11.4.2 The Mixed MLPG Methods Based on Independent
Interpolations of all the variables; §11.4.3 Conclusions; §11.5 Shear fl exible beams: seamless analysis from thick to thin beams; §11.6 Appendix I: The
Fortran code; XII Nonlinear Problems; §12.1 Introduction; §12.2 Piecewise Linearization; §12.3 Solving by Collocation; §12.3.1 The Newton-Raphson
Iterative Solution Procedure; §12.4 Subdomain Method; §12.5 The Finite Volume Method; §12.6 The Finite Element Method; §12.7 The Boundary Ele-
ment Method; §12.8 The Mixed MLPG method; XIII Eigen-Value Problems, Bifurcation Buckling, Vibration, & Transient Dynamic Response; §13.1
Bifurcation Buckling; §13.2 Linear Free & Forced Vibration; §13.3 Direct Integration with respect to the Time Variable.

Part II The Poisson & Helmholtz Equations: FEM, BEM, & Meshless Methods
XIV The Poisson & Helmholtz Equations: Finite Element, FIELD- Boundary Element, & Meshless Methods; §14.1 Introduction; §14.2 The Finite
Volume Method for the Poisson Equation; §14.3 The Galerkin FEM for the Poisson Equation; §14.4 The MLPG Method for Domain Discretization;
§14.4.1 The moving least-squares approximation scheme in 2 & 3 Dimensions; §14.4.2 The infl uences of the type of weight function, and of the geom-
etry of the weight-function support domain; §14.4.3 Shepard functions; §14.5 The partition of unity (PU) methods; §14.6 Reproducing kernel particle
interpolation (RKPM); §14.7 Compactly supported radial basis functions (CS-RBFs); §14.8 Smoothed particle hydrodynamics; §14.9 Interpolation
errors in meshless interpolations; §14.10 Summary of meshless interpolations of trial functions; §14.11 The Meshless Local Petrov-Galerkin (MLPG)
Method; §14.12 The imposition of essential boundary condition in the MLPG approach; §14.13 The Boundary Element Method for the Poisson Equation;
§14.14 Summary; XV The Boundary Element and the MLPG Method for the Discretization of Boundary/Integral Equations (BIE); §15.1 Introduction;
§15.2 Weakly-singular traction & displacement BIE in 3-D solid mechanics; §15.3 MLPG approaches for solving the weakly-singular BIEs; §15.3.1 The
MLPG approach; §15.3.2 Variants of the MLPG/BIE: several types of interpolation (trial) and test functions, and integration schemes; §15.3.3 Closure;
§15.4 Numerical experiments; §15.4.1 Cube under uniform tension; §15.4.2 3D Lame problem; §15.4.3 A concentrated load on a semi-infi nite space
(Boussinesq problem); §15.4.4 Non-planar crack growth; §15.4.5 Closure; XVI Non-Hyper-Singular Boundary Integral Equations For Acoustics, &
Their Solutions Through BEM, & MLPG/BIE Methods; §16.1 Introduction; §16.2 The governing wave equation, and its fundamental solution; §16.3
Boundary integral equations for φ, and φ,κ; §16.4 Numerical results; §16.5 Direct BEM Discretizations of R-φ-BIE & R-q-BIE; §16.6 Conclusion; §16.7

Appendix: The Matlab code for BIEs; References

"Meshfree Approximation Methods with MATLAB (Interdisciplinary Mathematical Sciences) (Interdisciplinary Mathematical Sciences)" (Gregory F. Fasshauer)

OBJECTIVE: detail implementation scheme and guideline for further developement