A hybrid finite element-Laplace transform method is implemented to analyze the time domain electromagnetic scattering induced by a 2-D overfilled cavity embedded in the infinite ground plane.The algorithm divides the ...A hybrid finite element-Laplace transform method is implemented to analyze the time domain electromagnetic scattering induced by a 2-D overfilled cavity embedded in the infinite ground plane.The algorithm divides the whole scattering domain into two,interior and exterior,sub-domains.In the interior sub-domain which covers the cavity,the problem is solved via the finite element method.The problem is solved analytically in the exterior sub-domain which slightly overlaps the interior subdomain and extends to the rest of the upper half plane.The use of the Laplace transform leads to an analytical link condition between the overlapping sub-domains.The analytical link guides the selection of the overlapping zone and eliminates the need to use the conventional Schwartz iteration.This dramatically improves the efficiency for solving transient scattering problems.Numerical solutions are tested favorably against analytical ones for a canonical geometry.The perfect link over the artificial boundary between the finite element approximation in the interior and analytical solution in the exterior further indicates the reliability of the method.An error analysis is also performed.展开更多
Direct Simulation Monte Carlo(DSMC)methods for the Boltzmann equation employ a point measure approximation to the distribution function,as simulated particles may possess only a single velocity.This representation lim...Direct Simulation Monte Carlo(DSMC)methods for the Boltzmann equation employ a point measure approximation to the distribution function,as simulated particles may possess only a single velocity.This representation limits the method to converge only weakly to the solution of the Boltzmann equation.Utilizing kernel density estimation we have developed a stochastic Boltzmann solver which possesses strong convergence for bounded and L∞solutions of the Boltzmann equation.This is facilitated by distributing the velocity of each simulated particle instead of using the point measure approximation inherent to DSMC.We propose that the development of a distributional method which incorporates distributed velocities in collision selection and modeling should improve convergence and potentially result in a substantial reduction of the variance in comparison to DSMC methods.Toward this end,we also report initial findings of modeling collisions distributionally using the Bhatnagar-Gross-Krook collision operator.展开更多
Here considered is the problem of transient electromagnetic scattering from overfilled cavities embedded in an impedance ground plane.An artificial boundary condition is introduced on a semicircle enclosing the cavity...Here considered is the problem of transient electromagnetic scattering from overfilled cavities embedded in an impedance ground plane.An artificial boundary condition is introduced on a semicircle enclosing the cavity that couples the fields from the infinite exterior domain to those fields inside.A Green’s function solution is obtained for the exterior domain,while the interior problem is solved using finite element method.Well-posedness of the associated variational formulation is achieved and convergence and stability of the numerical scheme confirmed.Numerical experiments show the accuracy and robustness of the method.展开更多
基金This workwas supported in part by the Air Force Office of Scientific Research.
文摘A hybrid finite element-Laplace transform method is implemented to analyze the time domain electromagnetic scattering induced by a 2-D overfilled cavity embedded in the infinite ground plane.The algorithm divides the whole scattering domain into two,interior and exterior,sub-domains.In the interior sub-domain which covers the cavity,the problem is solved via the finite element method.The problem is solved analytically in the exterior sub-domain which slightly overlaps the interior subdomain and extends to the rest of the upper half plane.The use of the Laplace transform leads to an analytical link condition between the overlapping sub-domains.The analytical link guides the selection of the overlapping zone and eliminates the need to use the conventional Schwartz iteration.This dramatically improves the efficiency for solving transient scattering problems.Numerical solutions are tested favorably against analytical ones for a canonical geometry.The perfect link over the artificial boundary between the finite element approximation in the interior and analytical solution in the exterior further indicates the reliability of the method.An error analysis is also performed.
基金This research is supported in part by the Air Force Office of Scientific Research,Project Number PEDRS001The views expressed in this article are those of the authors and do not reflect the official policy or position of the United States Air Force,Department of Defense,or the US Government。
文摘Direct Simulation Monte Carlo(DSMC)methods for the Boltzmann equation employ a point measure approximation to the distribution function,as simulated particles may possess only a single velocity.This representation limits the method to converge only weakly to the solution of the Boltzmann equation.Utilizing kernel density estimation we have developed a stochastic Boltzmann solver which possesses strong convergence for bounded and L∞solutions of the Boltzmann equation.This is facilitated by distributing the velocity of each simulated particle instead of using the point measure approximation inherent to DSMC.We propose that the development of a distributional method which incorporates distributed velocities in collision selection and modeling should improve convergence and potentially result in a substantial reduction of the variance in comparison to DSMC methods.Toward this end,we also report initial findings of modeling collisions distributionally using the Bhatnagar-Gross-Krook collision operator.
文摘Here considered is the problem of transient electromagnetic scattering from overfilled cavities embedded in an impedance ground plane.An artificial boundary condition is introduced on a semicircle enclosing the cavity that couples the fields from the infinite exterior domain to those fields inside.A Green’s function solution is obtained for the exterior domain,while the interior problem is solved using finite element method.Well-posedness of the associated variational formulation is achieved and convergence and stability of the numerical scheme confirmed.Numerical experiments show the accuracy and robustness of the method.
