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In this paper we study the temporal convergence of a locally implicit discontinuous Galerkin method for the time-domain Maxwell’s equations modeling electromagnetic waves propagation. Particularly, we wonder whether the method retains its second-order ordinary differential equation (ODE) convergence under stable simultaneous space-time grid refinement towards the true partial differential equation (PDE) solution. This is not a priori clear due to the component splitting which can introduce order...
In this paper we study the temporal convergence of a locally implicit discontinuous Galerkin method for the time-domain Maxwell’s equations modeling electromagnetic waves propagation. Particularly, we wonder whether the method retains its second-order ordinary differential equation (ODE) convergence under stable simultaneous space-time grid refinement towards the true partial differential equation (PDE) solution. This is not a priori clear due to the component splitting which can introduce order...
In this paper, we consider the back and forth nudging algorithm that has been introduced
for data assimilation purposes. It consists of iteratively and alternately solving forward
and backward in time the model equation, with a feedback term to the observations. We
consider the case of 1-dimensional transport equations, either viscous or inviscid, linear
or not (Burgers’ equation). Our aim is to prove some theoretical results on the
convergence,...
In this paper, we consider the back and forth nudging algorithm that has been introduced for data assimilation purposes. It consists of iteratively and alternately solving forward and backward in time the model equation, with a feedback term to the observations. We consider the case of 1-dimensional transport equations, either viscous or inviscid, linear or not (Burgers’ equation). Our aim is to prove some theoretical results on the convergence, and convergence properties, of this algorithm. We...
In this paper, we consider the back and forth nudging algorithm that has been introduced
for data assimilation purposes. It consists of iteratively and alternately solving forward
and backward in time the model equation, with a feedback term to the observations. We
consider the case of 1-dimensional transport equations, either viscous or inviscid, linear
or not (Burgers’ equation). Our aim is to prove some theoretical results on the
convergence,...
The Boltzmann–Poisson system modeling the electron flow in semiconductors is used to discuss the validity of the Child–Langmuir asymptotics. The scattering kernel is approximated by a simple relaxation time operator. The Child–Langmuir limit gives an approximation of the current-voltage characteristic curves by means of a scaling procedure in which the ballistic velocity is much larger that the thermal one. We discuss the validity of the Child–Langmuir regime by performing detailed numerical comparisons...
The Boltzmann–Poisson system modeling the electron flow in semiconductors
is used to discuss the validity of the Child–Langmuir asymptotics.
The scattering kernel is approximated by a simple relaxation time operator.
The Child–Langmuir limit gives an approximation of the current-voltage
characteristic curves by means of a scaling
procedure in which the ballistic velocity is much larger that the thermal one.
We discuss the validity of the Child–Langmuir regime by performing
detailed numerical...
We are concerned with the structure of the operator corresponding to the Lax–Friedrichs method. At first, the phenomenae which may arise by the naive use of the Lax–Friedrichs scheme are analyzed. In particular, it turns out that the correct definition of the method has to include the details of the discretization of the initial condition and the computational domain. Based on the results of the discussion, we give a recipe that ensures that the number of extrema within the discretized version of...
We are concerned with the structure of the operator
corresponding to the Lax–Friedrichs method.
At first, the phenomenae which may arise by the
naive use of the Lax–Friedrichs scheme are analyzed.
In particular, it turns out that the correct
definition of the method has to include the details
of the discretization of the initial condition
and the computational domain. Based on the results of the
discussion, we give a recipe that ensures that the
number of extrema within the discretized version...
We study the use of a GPU for the numerical approximation of the curvature dependent flows of graphs - the mean-curvature flow and the Willmore flow. Both problems are often applied in image processing where fast solvers are required. We approximate these problems using the complementary finite volume method combined with the method of lines. We obtain a system of ordinary differential equations which we solve by the Runge-Kutta-Merson solver. It is a robust solver with an automatic choice of the...
The initial boundary value problem for a beam is considered in the Timoshenko model. Assuming the analyticity of the initial conditions, it is proved that the problem is solvable throughout the time interval. After that, a numerical algorithm, consisting of three steps, is constructed. The solution is approximated with respect to the spatial and time variables using the Galerkin method and a Crank–Nicholson type scheme. The system of equations obtained by discretization is solved by a version of...
The initial boundary value problem for a beam is
considered in the Timoshenko model. Assuming the analyticity
of the initial conditions, it is proved that the problem is
solvable throughout the time interval. After that, a numerical algorithm,
consisting of three steps, is constructed. The solution is
approximated with respect to the spatial and time variables using
the Galerkin method and a Crank–Nicholson type scheme. The system
of equations obtained by discretization is solved
by a version...
We present a method for the construction of artificial far-field boundary conditions for two- and three-dimensional exterior compressible viscous flows in aerodynamics. Since at some distance to the surrounded body (e.g. aeroplane, wing section, etc.) the convective forces are strongly dominant over the viscous ones, the viscosity effects are neglected there and the flow is assumed to be inviscid. Accordingly, we consider two different model zones leading to a decomposition of the original flow...
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