Jorge Ospino Portillo - Academia.edu (original) (raw)
Papers by Jorge Ospino Portillo
Applied Mathematics and Computation, 2018
En este artículo se demuestra que el Espacio Lp es un espacio de Banach; siguiendo el siguiente e... more En este artículo se demuestra que el Espacio Lp es un espacio de Banach; siguiendo el siguiente esquema: Demostrando que Lp es normado y que toda sucesión de Cauchy de elementos de Lp, converge en Lp, es decir que Lp es completo. Como caso particular, se muestra que para p = 2, L2, es un espacio de Hilbert
Mathematics, 2022
We consider the scattering of time-periodic electromagnetic fields by metallic obstacles, or the ... more We consider the scattering of time-periodic electromagnetic fields by metallic obstacles, or the eddy current problem. In this interface problem, different sets of Maxwell equations must be solved both in the obstacle and outside it, while the tangential components of both electric and magnetic fields are continuous across the interface. We describe an asymptotic procedure, applied for large conductivity, which reflects the skin effect in metals. The key to our method is a special integral equation procedure for the exterior boundary value problems corresponding to perfect conductors. The asymptotic procedure leads to a great reduction in complexity for the numerical solution, since it involves solving only the exterior boundary value problems. Furthermore, we introduce a FEM/BEM coupling procedure for the transmission problem and consider the implementation of Galerkin’s elements for the perfect conductor problem, and present numerical experiments.
This thesis deals with the coupling of finite elements and boundary elements for electromagnetic ... more This thesis deals with the coupling of finite elements and boundary elements for electromagnetic interface problems, especially the skin effect in R 3. The first part (Chapter 1) is dedicated to the study of transmission problems of electromagnetic waves in materials with strong contrast. We report the ideas which were developed by MacCamy and Stephan [30, 31], who consider the scattering of timeperiodic electromagnetic fields by metallic obstacles, the eddy current problem. In this interface problem different sets of Maxwell equations must be solved in the obstacle and outside, while the tangential components of both electric and magnetic fields are continuous across the obstacle surface. We present two solution procedures.One is an asymptotic procedure which applies for large conductivity and reflects the skin effect in metals. This asymptotic procedure gives for the computation of the solution of the transmission problem a great reduction in complexity since it involves solving only the exterior boundary value problem (perfect conductor problem). The latter is solved numerically by the boundary element method. We give numerical experiments which show the efficiency of this procedure. The other solution procedure is a new coupling method with finite elements and boundary elements which allows the use of standard, conforming test and trial functions which are easy to implement. In the second part (Chapters 2, 3, 4) we consider two different problems in the whole space R 3 , the scalar and the electromagnetic transmission problems. For both problems we prove a priori estimates. We calculate the terms of an asymptotic expansion of the electrical field and study its convergence. The ideas of this part are based on those of Peron [42], who considered a bounded exterior domain, while we extend his results to the case of an unbounded exterior domain. For this extension we use Beppo-Levi spaces with weights at infinity. The third part (Chapter 5) is concerned with a non-conforming fem/bem coupling to solve the two-dimensional eddy current problem for the time harmonic Maxwell's equations. We use Crouzeix-Raviart elements in the interior domain and piecewise linear and piecewise constant boundary elements on the interface boundary.
Applied Mathematics and Computation, 2018
En este artículo se demuestra que el Espacio Lp es un espacio de Banach; siguiendo el siguiente e... more En este artículo se demuestra que el Espacio Lp es un espacio de Banach; siguiendo el siguiente esquema: Demostrando que Lp es normado y que toda sucesión de Cauchy de elementos de Lp, converge en Lp, es decir que Lp es completo. Como caso particular, se muestra que para p = 2, L2, es un espacio de Hilbert
Mathematics, 2022
We consider the scattering of time-periodic electromagnetic fields by metallic obstacles, or the ... more We consider the scattering of time-periodic electromagnetic fields by metallic obstacles, or the eddy current problem. In this interface problem, different sets of Maxwell equations must be solved both in the obstacle and outside it, while the tangential components of both electric and magnetic fields are continuous across the interface. We describe an asymptotic procedure, applied for large conductivity, which reflects the skin effect in metals. The key to our method is a special integral equation procedure for the exterior boundary value problems corresponding to perfect conductors. The asymptotic procedure leads to a great reduction in complexity for the numerical solution, since it involves solving only the exterior boundary value problems. Furthermore, we introduce a FEM/BEM coupling procedure for the transmission problem and consider the implementation of Galerkin’s elements for the perfect conductor problem, and present numerical experiments.
This thesis deals with the coupling of finite elements and boundary elements for electromagnetic ... more This thesis deals with the coupling of finite elements and boundary elements for electromagnetic interface problems, especially the skin effect in R 3. The first part (Chapter 1) is dedicated to the study of transmission problems of electromagnetic waves in materials with strong contrast. We report the ideas which were developed by MacCamy and Stephan [30, 31], who consider the scattering of timeperiodic electromagnetic fields by metallic obstacles, the eddy current problem. In this interface problem different sets of Maxwell equations must be solved in the obstacle and outside, while the tangential components of both electric and magnetic fields are continuous across the obstacle surface. We present two solution procedures.One is an asymptotic procedure which applies for large conductivity and reflects the skin effect in metals. This asymptotic procedure gives for the computation of the solution of the transmission problem a great reduction in complexity since it involves solving only the exterior boundary value problem (perfect conductor problem). The latter is solved numerically by the boundary element method. We give numerical experiments which show the efficiency of this procedure. The other solution procedure is a new coupling method with finite elements and boundary elements which allows the use of standard, conforming test and trial functions which are easy to implement. In the second part (Chapters 2, 3, 4) we consider two different problems in the whole space R 3 , the scalar and the electromagnetic transmission problems. For both problems we prove a priori estimates. We calculate the terms of an asymptotic expansion of the electrical field and study its convergence. The ideas of this part are based on those of Peron [42], who considered a bounded exterior domain, while we extend his results to the case of an unbounded exterior domain. For this extension we use Beppo-Levi spaces with weights at infinity. The third part (Chapter 5) is concerned with a non-conforming fem/bem coupling to solve the two-dimensional eddy current problem for the time harmonic Maxwell's equations. We use Crouzeix-Raviart elements in the interior domain and piecewise linear and piecewise constant boundary elements on the interface boundary.