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N.G. Bourago (Burago) : code ASTRA


Code ASTRA (Automated System for Theoretical Research and Analysis)

1. What is ASTRA?

The code ASTRA provides numerical solution of 1,2,3D unsteady nonlinear problems in continuum mechanics using moving adaptive Eulerian-Lagrangian unstructured grids and the finite element method. It is not universal, but rather general (see Demo ) and flexible.

ASTRA simulates nonlinear processes

Following phenomenas are taken into account:

By using ASTRA it is possible to solve

 

2. What is the mathematical basis of ASTRA?

Code ASTRA is based upon the special version [1] of the finite element method. The major features are

3. Physical basement of ASTRA

All equations are formulated in actual configuration settings, which are common for solid and fluid mechanics, and the arbitrary moving adaptive coordinates and adaptive unstructured grids are used. The Eulerian, Lagrangian or mixed descriptions of motion for various parts of the solution region are used simultaneously in accordance with physical statement of particular problem. For proper description of continuum motion in case of multiple moving and free boundaries the mathematical techniques of continuous and discrete markers are implemented.

While the code ASTRA was in progress (since 1976) the appropriate constitutive equations were developed on the basis of thermodynamical laws for irreversible nonequilibrated processes. So the set of new constitutive equations is used to get an adequate description of a variety of processes such as sintering, damage or/and softening of materials. Due to convenient arrangement and flexibility of the code ASTRA it is easy to quickly make multiple checkups of many strange and even "mad" physical ideas, arised in attempts to simulate various mechanical phenomenas.

4. Numerical methods.

Quasi-second order explicit and implicit finite difference schemes in time are implemented. It is important to remark that the major line of ASTRA which states that the preference always should be given to most simple, identical and robust algorithms has the very pleasant outcome: algorithms for very different areas in continuum mechanics such as solid mechanics, incompressible fluid and compressible gas dynamics, theory of shallow water, filtration and diffusion problems appeared finally to be almost the same.

All implicit schemes use the conjugate gradient non-matrix method with preconditioning using the diagonal approximation of stiffness matrix.

It:

Each conjugate gradient iteration is realized like a routine time step in explicit methods. Finite and not big number of such iterations is required to reach high accuracy of the solution. The conservative Lagrange multiplier and penalty techniques are used to calculate contact interactions in solid mechanics and to satisfy the incompressibility condition for incompressible solid and liquid medii.

Nonlinear artificial viscosity terms are added into equations to provide the stability and the accuracy of the algorithms. The analysis of Hirt-Shokin approximations of finite element schemes and exponential correction technique lay in the basement of the choice of such terms. In addition moving adaptive grids also serve to decrease approximation errors.

All algorithms contain mainly arithmetical operations with vectors of high dimension, which relates to the number of unknowns. Therefore the code ASTRA was easily vectorized more then decade ago.

All algorithms have on-line accuracy control.

5. Why ASTRA is a good code?

In contrast to many application codes the code ASTRA:

ALSO code ASTRA has following important features:

6. Computer platforms and basic software.

Code ASTRA is known since 1977 (by name ASTRA since 1983). It works (worked) on the following computers:

Main ASTRA language is FORTRAN-77. Some other languages (C and Assembler) are used only for low level subroutines to support hardware interface. Any 32-bit compiler can be used to make the code ASTRA alive.

The code ASTRA is not commercial. All rights reserved by the creator N.G.Bourago.

7. References

Bourago N.G., Kukudzhanov V.N. "Solution of elasto-plastic problems by finite element method. HydroCode ASTRA", Preprint of the Institute for Problems in Mechanics of AS USSR, n.326, 1988,pp. 1-63

Bourago N.G., Kukudzhanov V.N. "Solution of elasto-plastic problems by finite element method. HydroCode ASTRA", in book: Computer Mechanics of Solids, vol. 2, Nauka, 1991, pp.78-122

Bourago N., Computer code "ASTRA" for nonlinear problems in continuum mechanics, Proc. of NORDIC-7 seminar, Trondheim, 1994 (Short description in English)

Complete list of references can be found on my WebPage: http://www.ipmnet.ru/~burago


Contact information:
Email:
burago@ipmnet.ru Web: http://www.ipmnet.ru/~burago Tel: +7 (495) 434-41-35 Fax: +7 (495) 739-95-31
Mail address: Institute for Problems in Mechanics of RAS, prospect Vernadskogo 101, b1, Moscow, 119526, Russia


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