Express Tour

            Finite Element and Numerical Methods with Integrable / Differentiable Objects.
       Express Tour

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sftrolley{1].gif (15971 bytes) The express tour guides you through foundation classes in VectorSpace C++ Library and some shortest application examples in computational linear algebra, optimization, variational methods, and finite element methods. A more complete description of these classes and application examples can be found under "Online Workbook" navigation button in the home page. The workbook has more than 600 pages in PDF format.

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	C0 Type for Expressive C++ Programming (in PDF). --What are the submatrix, and basis objects?
	C1 and C2 Types for Differentiable Objects (in PDF). --What are the differentiable objects?
	H0, H1, and H2 Types for Integrable / Differentiable Objects (in PDF). --What are the integrable / differentiable objects?

Free Express Tour- II
through some application examples in Computational Linear Algebra, Optimization, and Variational Methods.

Computational Linear Algebra :

	basis expression,
	line-fitting,
	principal component analysis

Numerical Optimization :

	linear programming,
	conjugate gradient method,
	quasi-Newton (BFGS) method

Variational Methods :

	second-order ODE,
	Poisson equation

Free Express Tour- III
through two basic element formulations in Finite Element Methods.

Heat Conduction

Plane Elasticity (10 implementations on 3 formulations)

	B-matrix formulation,
	indicial notation formulation,
	coordinate-free tensorial formulation

The Express Tour on Plane Elasticity deserves special attention. Firstly, the B-matrix formulation is a set of examples that when finite element formula are given explicitly, VectorSpace C++ Library is very flexible that multiple ways of implementations from very different perspectives are possible. Secondly, the implementation examples in the indicial notation formulation demonstrate that the VectorSpace C++ Library can be used as a Rapid-Proto-Typing Tool. In such a case, a sequence of optimization steps can be taken later until no VectorSpace C++ Library features are used in the final production codes. Therefore, the finial production codes can be made to run as fast as possible. Finally, for a case as in a research project, no canonical finite element formula such as B-matrix formulation is available. You are facing with a PDE that is not discussed in any finite element text. The implementation example for the coordinate-free tensorial formulation shows that, as scientists, engineers or mathematicians, you are expected to derive the most general equations from the basic physical principles, and then these equations can be most efficiently implemented by taking the advantage of the VectorSpace C++ Library and the object-oriented programming method per se. The use of Vectorspace C++ Library maximizes programming efficiency in that the C++ statements directly mimic the advanced mathematical expressions.

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