By Annamaria Cividini (eds.)
The NUMGE98 convention introduced jointly senior and younger researchers, scientists and training engineers from eu and abroad international locations, to proportion their wisdom and event at the a variety of points of the research of Geotechnical difficulties via Numerical tools. The papers tackle a large spectrum of geotechnical difficulties, together with tunnels and underground openings, shallow and deep foundations, slope balance, seepage and consolidation, partly saturated soils, geothermal results, constitutive modelling, etc.
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Additional info for Application of Numerical Methods to Geotechnical Problems: Proceedings of the Fourth European Conference on Numerical Methods in Geotechnical Engineering Numge98 udine, Italy October 14–16, 1998
M. Smith 32 Full GMRES has been coded and the implications of using it for geotechnical engineering problems are considered later. 6 ALGORITHM COSTS IN TIME AND MEMORY The computational cost of diagonal preconditioning in the conjugate gradient method is negligible and so CG and PCG have essentially the same cost in time and memory. Similarly, MINRES costs essentially the same in time, but the memory resources are somevvhatincreased. Preconditioning in the minimum residual method (PMINRES) does hovvever incur significant extra costs in computer time and in memory : 17 @ NEQ-long vectors compared to 12 in MINRES and 9 in PCG in the author's implementations.
Proc. 7th ICSMFE. Mexico. State-of-the-Art Volume, 225-290. Pender, M. J. (1980). Elastic solutions for a deep circular tunnel. Geotechnique 30,216-222. Sagaseta, C. (1987). Analysis of undrained soil deformation due to ground loss. Geotechnique 37:3,301-320. Sagaseta, C. (1988). Author's reply. Geotechnique 38:4,647-649. M. Sanchez-Alciturri, C. Gonzalez, A. L6pez, P. Gomez and R. Pina (1999). Soil deformations due to the excavation of two parallel underground caverns. Proc. 12th Eur. Conf. Soil Mech.
J,Q and rare vectors of length NEQ, the number of equations to be solved, while a and f3 are scalars. The main part of the solution process can be seen to consist of a matrix-vector multiplication (12) followed by a series of operations on vectors. Equation (12) can be solved in two main ways, each of which conserves storage. Either A can be assembled in sparse form, with pointers to its non-zero entries, or the operation called for by equation (12) can be carried out "element-by-element" in which case A is never assembled at all, and only the individual element matrices on the left hand side of equations (9) and (1 0) are involved in the matrixvector multiplication.
Application of Numerical Methods to Geotechnical Problems: Proceedings of the Fourth European Conference on Numerical Methods in Geotechnical Engineering Numge98 udine, Italy October 14–16, 1998 by Annamaria Cividini (eds.)