Sharp interface limit for a phase field model in structural optimization

We formulate a general shape and topology optimization problem in structural optimization by using a phase field approach. This problem is considered in view of well-posedness and we derive optimality conditions. We relate the diffuse interface problem to a perimeter penalized sharp interface shape optimization problem in the sense of $\Gamma$-convergence of the reduced objective functional. Additionally, convergence of the equations of the first variation can be shown. The limit equations can also be derived directly from the problem in the sharp interface setting. Numerical computations demonstrate that the approach can be applied for complex structural optimization problems

Numerical solution of an inverse problem of determining the parameters of a source of groundwater pollution

The article deals with an inverse problem of determining parameters of groundwater pollution sources. We test three ways to solve the problem on the simulated data for a simple case of contamination. We discover that, in the presence of noise in the data of the inverse problem, the first method does not produce satisfactory recovery results, while the second and third ones are comparable in accuracy of the recovery of required parameters. Taking into account the ease of implementation, the speed of computing and parallelization feasibility the second method of solving the inverse problem is found to be most preferable. We also propose a method of finding pollution parameters in general case..

Solution of the Inverse Problem of Subsurface Electric Exploration for Horizontally Stratified Medium

In this paper, we offer the generalization of the known technique of the construction of the gradient of the residual functional based on the statement of the conjugate problem for the case when the unknown function is complex valued. The notion of the reference frequency of the medium is introduced. Knowing the value of the reference frequency lets us judge the possibility of simultaneous definition of the dielectric permittivity and conductivity

Determining kinetic parameters of a block coal bed gas by solving inverse problem based on data of borehole gas measurements

International audienceIn the framework of the developed and implemented nonlinear geomechanical model of a coal bed having block structure, describing gas inflow, the authors propose the method for quantitative estimate of gas content as well as diffusion and mass exchange coefficients based on solution of inverse problems using pressure measurements taken in shut-in borehole in the “pressure drop” mode. Besides the main function, the set problem had an auxiliary objective function with the less number of arguments. Numerical experiments with synthetic input data yield that the auxiliary objective function has a number of local minimums. The authors also put forward a technique of finding global minimum that provides the set problem solution

Estimating diffusion-capacity parameters of a coal bed using the gas pressure measured in a hole and the solution of an inverse problem

International audienceA geomechanical model is proposed for gas emission from a coal bed with block structure. Some coefficient inverse problem is formulated for finding the initial gas content as well as the diffusion and mass transfer coefficients from the measured pressure in a well. The solvability of this problem is tested, and the additional data on the gas-kinetic characteristics of the coal bed are shown to be necessary for the inverse problem to have a unique solution