In this paper, we give the state of the art for the so called “mixed spectral elements” for Maxwell＇s equations. Several families of elements, such as edge elements and discon-tinuous Galerkin methods （DGM） are p...In this paper, we give the state of the art for the so called “mixed spectral elements” for Maxwell＇s equations. Several families of elements, such as edge elements and discon-tinuous Galerkin methods （DGM） are presented and discussed. In particular, we show the need of introducing some numerical dissipation terms to avoid spurious modes in these methods. Such terms are classical for DGM but their use for edge element methods is novel approach described in this paper. Finally, numerical experiments show the fast and low-cost character of these elements.展开更多
The paper addresses the construction of a non spuriousmixed spectral finiteelement(FE)method to problems in the field of computational aeroacoustics.Basedon a computational scheme for the conservation equations of lin...The paper addresses the construction of a non spuriousmixed spectral finiteelement(FE)method to problems in the field of computational aeroacoustics.Basedon a computational scheme for the conservation equations of linear acoustics,the extensiontowards convected wave propagation is investigated.In aeroacoustic applications,the mean flow effects can have a significant impact on the generated soundfield even for smaller Mach numbers.For those convective terms,the initial spectralFE discretization leads to non-physical,spurious solutions.Therefore,a regularizationprocedure is proposed and qualitatively investigated bymeans of discrete eigenvaluesanalysis of the discrete operator in space.A study of convergence and an applicationof the proposed scheme to simulate the flow induced sound generation in the processof human phonation underlines stability and validity.展开更多
After setting a mixed formulation for the propagation of linearized water waves problem,we define its spectral element approximation.Then,in order to take into account unbounded domains,we construct absorbing perfectl...After setting a mixed formulation for the propagation of linearized water waves problem,we define its spectral element approximation.Then,in order to take into account unbounded domains,we construct absorbing perfectly matched layer for the problem.We approximate these perfectly matched layer by mixed spectral elements and show their stability using the“frozen coefficient”technique.Finally,numerical results will prove the efficiency of the perfectly matched layer compared to classical absorbing boundary conditions.展开更多
文摘In this paper, we give the state of the art for the so called “mixed spectral elements” for Maxwell＇s equations. Several families of elements, such as edge elements and discon-tinuous Galerkin methods （DGM） are presented and discussed. In particular, we show the need of introducing some numerical dissipation terms to avoid spurious modes in these methods. Such terms are classical for DGM but their use for edge element methods is novel approach described in this paper. Finally, numerical experiments show the fast and low-cost character of these elements.
文摘The paper addresses the construction of a non spuriousmixed spectral finiteelement(FE)method to problems in the field of computational aeroacoustics.Basedon a computational scheme for the conservation equations of linear acoustics,the extensiontowards convected wave propagation is investigated.In aeroacoustic applications,the mean flow effects can have a significant impact on the generated soundfield even for smaller Mach numbers.For those convective terms,the initial spectralFE discretization leads to non-physical,spurious solutions.Therefore,a regularizationprocedure is proposed and qualitatively investigated bymeans of discrete eigenvaluesanalysis of the discrete operator in space.A study of convergence and an applicationof the proposed scheme to simulate the flow induced sound generation in the processof human phonation underlines stability and validity.
文摘After setting a mixed formulation for the propagation of linearized water waves problem,we define its spectral element approximation.Then,in order to take into account unbounded domains,we construct absorbing perfectly matched layer for the problem.We approximate these perfectly matched layer by mixed spectral elements and show their stability using the“frozen coefficient”technique.Finally,numerical results will prove the efficiency of the perfectly matched layer compared to classical absorbing boundary conditions.
