Finite Element and Numerical Methods with Integrable / Differentiable Objects.
      
      

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c0.lib,  a C++ class library with scalar, vector, matrix, subvector, submatrix and basis objects.  c0.lib is the kernel of vs.lib. The Application Examples in c0.lib include matrix solvers (including LU decomposition, Cholesky decomposition, and QR decomposition), finite difference method, least squares, inverse problem (such as computer tomography), eigenvalue problems, and  factor analysis (by singular value decomposition).

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vs.lib application source codes
Table of Contents

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All Example Application Source Codes in VectorSpace C++ Library (vs.lib)

Click here to view the workbook for the application examples.

1. Numerical Linear Algebra (source files in "C0/")
   Matrix Computations (Matrix Algebra,  LU, Cholesky, QR, Singularvalue Decomposition, Eigenvalue)
   Methods of Least Squares (Data fitting)
   Inverse Problems (Tomography)
   Finite Difference Method (Heat Conduction)
   Principal Component Analysis (Morphology, Stock Market, Scholastic Achievement Analyses)

2. Optimization (source files in "Cn/")
   Linear Programming (Basic Set & Active Set Methods)
   Unconstrained Optimization (Newton's, Steepest Descent, Conjugate Gradient, Quasi-Newton BFGS Methods)
   Constrained Optimization (Reduced Gradient, Gradient Projection, Lagrange, Range / Null Spaces, Penalty Function, Augmented Lagrangian, Perturbed Lagrangain Methods)

3. Variational Methods (source files in "Hn/")
   Rayleigh-Ritz Method (2nd & 4th-order ODE, and  Poisson Equation)
   Weighted Residual Method (Point-Collocation, Subdomain Collocation, Method of Moment, Bubnov-Galerkin, Petrov-Galerkin, and Least Squares Methods)
   Boundary Solution Method (Trefftz & Boundary Element Methods)
   Transient Problem (Parabolic & Hyperbolic Equations)

4. Finite Element Method (source files in "fe/")
   Preliminary : 2nd-order & 4th-order, Nonlinear ODEs / Transient / Matrix Substructuring
   (1-D Elements: Linear Line, Quadratic Line, Axisymmetrical cylindrical. Formulations: Irreducible, Mixed, Lagrangian multiplier, Penalty Function, Galerkin, Least Squares)
   Basics: Heat Conduction / Potential Flow / Elasticity / Stokes Flow / Plate Bending
   (2-D Elements: Triangular, bilinear, 4-to-9 nodes Lagragian, Formulations: B-Matrix (strain-displacement matrix), Indicial Notation (in l-m), Coordinate-Free Tensorial Notation, Post-processing: Nodal Reaction, Stress & Strain on both Gauss Point and Nodal Projection, Selective Reduced Integrations: Shear-Locking & Dilatation-Locking, Patch Test: Consistency, Stability, Weak, Higher-Order, and  Conforming/Non-conforming Elements)
   Advanced: Mixed & Hybrid Methods / Contact Mechanics / Finite Elastoplastic Deformation
   (Mixed Methods: Helliger-Reissner / Hu-Washizu Variational Principles, Incompressible u-p & Incompressible u-p-e_v Formulations, B Formulations, Hourglass Elements, Hybrid Methods: Irreducible Subdomain, Pian-Sumihara Element, Reissner-Mindlin Plate Theory: q-w irreducible and q-S-w Mixed Formulations, Contact Mechanics: Mixed Formulation, Contact Searching Algorithm, Elastoplasticity: Incremental Loading algorithm, Radial Return Mapping alogrithm, Finite Deformation: Finite Stress-Strain Measures, Multiplicative Elastoplastic Decomposition, Covariant Algorithm)
   

5. Finite Element Library (source files in "felib/")

    The free source codes of "fe.lib" under the directory "felib/" is used as an example, for the community of numerical computation, to demonstrate the strength of the current programming paradigms; the object-oriented analysis and design and the framework-based software development.

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