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Energy estimates and numerical verification of the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell’s system

100%

Beilina L.

Open Mathematics

2013

tom 11

nr 4

702-733

We rigorously derive energy estimates for the second order vector wave equation with gauge condition for the electric field with non-constant electric permittivity function. This equation is used in the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell’s system. Our numerical experiments illustrate efficiency of the modified hybrid scheme in two and three space dimensions when the method is applied for generation of backscattering data in the reconstruction of the electric permittivity function.

An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data

63%

Koshev N., Beilina L.

Open Mathematics

2013

tom 11

nr 8

1489-1509

We propose an adaptive finite element method for the solution of a linear Fredholm integral equation of the first kind. We derive a posteriori error estimates in the functional to be minimized and in the regularized solution to this functional, and formulate corresponding adaptive algorithms. To do this we specify nonlinear results obtained earlier for the case of a linear bounded operator. Numerical experiments justify the efficiency of our a posteriori estimates applied both to the computationally simulated and experimental backscattered data measured in microtomography.

Ograniczanie wyników

2 Open Mathematics

2 Beilina L.

1 Koshev N.

2 2013

Wyniki wyszukiwania

Energy estimates and numerical verification of the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell’s system

An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data