Институт вычислительной математики и математической геофизики СОРАН

Abstracts

numerical solution of DE and IE

We formulate the problem on propagation of long waves in a domain of arbitrary form with the sufficiently smooth boundary on a sphere. The boundary consists of “solid” parts passing along the coastline and “liquid” parts passing through the water area. We assume free surface level observation data on some part of “liquid” boundary is known.

In general case the boundary condition on “liquid” part of boundary contains unknown boundary function, which must be found together with component of velocity vector and free surface level. We put an assimilation observation data problem by Prof. V.I. Agoshkov methodology. To solve our ill-posed inverse problem an approach, based on optimal control methods and adjoint equations theory, is used.

We consider two family of optimal control problem with regularization to determine of minimum of calculating error between numerical free surface level and observation one with respect to some special norm. The iterative numerical method to recovery of the boundary function (and, hence, to obtaining a general solution of our problem) is suggested. The method consists in iterative improvement of the boundary function by numerical solution of direct and adjoint problems by turns.

Numerical solution of direct and adjoint problems is based on finite elements method. Parallel software using MPI was created. Performance of two popular implementations of MPI was compared and studied the behavior of our software when using various ways of memory allocation.

The work was supported by Russian Foundation of Fundamental Researches (grant 11-01-00224-a) and by SB RAS (Integration Project 26)

Note. Abstracts are published in author's edition

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