| Budget Amount *help |
¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 1993: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1992: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Research Abstract |
1. Study of the control for the wave equation with BIEM
A computer code for 2 dimensional wave equation in time domain is developed. This code is then modified into a program to obtain the exact control for the wave equation with the help of HUM (the Hilbert uniqueness method). This approach is in contrast to FEM in that it does not require the analysis of the backward problem. Also, the obtained code is remarkable in terms of its simplicity high speed and high accuracy. We found that the solution of axisymmetric problems can be obtained with this approach. In non-axisymmetric problems with many degrees of freedom for the unknown functions, however, the use of Tikhonov's regularisation is necessary.
Although the original plan included control problems with constrains, we felt it would be more worth-while to consider minimization of the sum of L^2 norms of the field variable (pressure) and the boundary control. This is because one is interested in reducing the pressure level in noise control problems. Some theoretical consideration reduces this problem to a system of PDEs similar to the so called optimal system. As we found, however, the numerical calculation for this problem with BIEM is rather unstable, and could obtain numerical solutions only in simple problems.
2. Study of the control for the plate equation with BIEM
An analysis similar to those in 1.was carried out in the context of the dynamical equation of plate. The Dirichlet control in this problem drives the plate to rest by prescribing appropriate boundary deflection and slope. A numerical study is carried out in an axisymmetric problem. It is found that the choice of the time shape functions controls the stability of the numerical analysis. We could obtain a good result with piecewise linear (constant) shape functions for the Dirichlet (Neumann) data, with the help of the Tikhonov regularisation.
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