In this much-expanded second edition, author Yair Shapira presents new applications and a substantial extension of the original object-oriented framework to make this popular and comprehensive book even easier to understand and use. It not only introduces the C and C++ programming languages, but also shows how to use them in the numerical solution of partial differential equations (PDEs). The book leads readers through the entire solution process, from the original PDE, through the discretization stage, to the numerical solution of the resulting algebraic system. The high level of abstraction available in C++ is particularly useful in the implementation of complex mathematical objects, such as unstructured mesh, sparse matrix, and multigrid hierarchy, often used in numerical modeling. The well-debugged and tested code segments implement the numerical methods efficiently and transparently in a unified object-oriented approach.The quadratic finite elements considered here have the same triangular shape as before. ... a particular finite element can be defined in terms of three typical ( standard) nodal functions, defined in the reference triangle in Figure 12.2, which isanbsp;...
|Title||:||Solving PDEs in C++|
|Publisher||:||SIAM - 2012-06-07|