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# Iterative Processes for the Finite Element Method Method In Hydrology

IP.com Disclosure Number: IPCOM000078241D
Original Publication Date: 1972-Dec-01
Included in the Prior Art Database: 2005-Feb-25
Document File: 2 page(s) / 25K

IBM

## Related People

Gambolati, G: AUTHOR

## Abstract

This is an investigation on the triangular meshes which produce diagonally dominant matrices for the finite element method in hydrology. The above property allows the resolution of the final linear systems by means of rapidly converging iterative processes.

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Iterative Processes for the Finite Element Method Method In Hydrology

This is an investigation on the triangular meshes which produce diagonally dominant matrices for the finite element method in hydrology. The above property allows the resolution of the final linear systems by means of rapidly converging iterative processes.

In Bidimentional confined flow the governing differential equation is:

(Image Omitted)

where upsilon, k and c are the hydraulic head, the permeability and the storage coefficient.

Using triangular networks. the numerical development leads to a final system whose matrix is expressed in the form: [D] = 2 over Delta t [p] + [H]. where triangular t is the time step and [H] and [P] are matrices obtained by properly assembling the local matrices [h] and [p] computed over each triangle.

If the local matrix [h] + 2[p] over Delta t is diagonally dominant, the same property is satisfied by the global matrix [D]. By following the previous criterion it is derived that the matrix [D] is diagonally dominant in isotropic domain if:

(Image Omitted)

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