Computer aided design system

Details Computer aided design system Computer aided design system

1996-07-31

1998-05-19

Nguyen, Phu K.

Computer graphics processing and selective visual display system

Computer graphics processing

Three-dimension

345420, G06T 1700

Patent

active

057541817

ABSTRACT:
A computer-aided design system in which a mechanical quantity of a structure can be determined from stored geometrical representation of the structure, the material properties thereof and the loads imposed thereon, comprising: generating data describing a structure as a mesh; generating by application of the finite element method to the mesh, the elements of a stiffness matrix, a loading vector, and a vector including an associated degree of freedom index for each row and column of the stiffness matrix, generating from the stiffness matrix and the loading vector elements of matrix A and a right hand-side vector f, where A and f are related through the relation Ax=f, the vector x representing a mechanical quantity at a plurality of points of the mesh; and a linear solver of the preconditioned conjugate gradient type for generating, for subsequent processing or display, the elements of the vector x from A and f using a preconditioning matrix, the system being characterised in that the linear solver comprises generating a principal submatrix from the stiffness matrix by setting to zero those elements therein in positions such that the degree of freedom index associated with their row is not equal to the degree of freedom index associated with their column and generating the preconditioning matrix from the principal submatrix.

REFERENCES:
patent: 5136538 (1992-08-01), Karmarker et al.
Ralston, A. (Ed.), Encyclopedia of Computer Science and Engineering, Van Nostrand Reinhold Company Inc., pp. 631-632, 927-932, 1983.
McCallum, P., "Getting Better Results from Linear FEA", Machine Design, v. 64, n. 2, pp. 123-126, Feb. 20, 1992.
Saad, Y., "On the Lanczos Method for Solving Symmetric Linear Systems with Several Right-Hand Sides", Mathematics of Computation, v. 48, n. 178, pp. 651-662, Apr., 1987.

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