An Energy Based Discontinuous Galerkin Method for Coupled Elasto-Acoustic Wave Equations in Second Order Form

We consider wave propagation in a coupled fluid-solid region, separated by a static but possibly curved interface. The wave propagation is modeled by the acoustic wave equation in terms of a velocity potential in the fluid, and the elastic wave equation for the displacement in the solid. At the fluid solid interface, we impose suitable interface conditions to couple the two equations. We use a recently developed, energy based discontinuous Galerkin method to discretize the governing equations in space. Both energy conserving and upwind numerical fluxes are derived to impose the interface conditions. The highlights of the developed scheme include provable energy stability and high order accuracy. We present numerical experiments to illustrate the accuracy property and robustness of the developed scheme

Novel Meteor Simulation and Observation Techniques that Emerged from Big-Sky-Earth COST Action

The cooperation of scientists in Big-Sky-Earth COST Action creates an emergent group of researchers with relation to meteor science. Selected cases of development of novel approaches and techniques for meteor simulation and observation are presented

Controlled time integration for numerical simulation of meteor radar reflections

We model meteoroids entering the Earth׳s atmosphere as objects surrounded by non-magnetized plasma, and consider efficient numerical simulation of radar reflections from meteors in the time domain. Instead of the widely used finite difference time domain method (FDTD), we use more generalized finite differences by applying the discrete exterior calculus (DEC) and non-uniform leapfrog-style time discretization. The computational domain is presented by convex polyhedral elements. The convergence of the time integration is accelerated by the exact controllability method. The numerical experiments show that our code is efficiently parallelized. The DEC approach is compared to the volume integral equation (VIE) method by numerical experiments. The result is that both methods are competitive in modelling non-magnetized plasma scattering. For demonstrating the simulation capabilities of the DEC approach, we present numerical experiments of radar reflections and vary parameters in a wide range.peerReviewe

Controllability techniques for the Helmholtz equation with spectral elements

We consider the use of controllability techniques to solve the Helmholtz equation. Instead of solving directly the time-harmonic equation, we return to the corresponding time-dependent equation and look for time-periodic solution. The convergence is accelerated with a control technique by representing the original time-harmonic equation as an exact controllability problem for the time-dependent wave equation. This involves finding such initial conditions that after one time-period the solution and its time derivative would coincide with the initial conditions. Spatial discretization is done with spectral element method. It allows convenient treatment of complex geometries and varying material properties. The basis functions are higher order Lagrange interpolation polynomials, and the nodes of these functions are placed at Gauss-Lobatto collocation points. The integrals in the weak form of the equation are valuated with the corresponding Gauss-Lobatto quadrature formulas. As a consequence of the choice, spectral element discretization leads to diagonal mass matrices which significantly improves the computational efficiency of the explicit time-integration used. Moreover, when using higher order elements, same accuracy is reached with less degrees of freedom than when using lower order finite elements. After discretization, exact controllability problem is reformulated as a least-squares optimization problem, which is solved with a preconditioned conjugate gradient algorithm. Each conjugate gradient iteration requires computation of the gradient of the least-squares functional, which involves the solution of the state equation and the corresponding adjoint equation, solution of a linear system with the preconditioner, and some matrix-vector operations. Computation of the gradient of the functional is an essential point of the method, and we have done it with the adjoint state technique directly for the discretized problem. Algebraic multigrid method is used for preconditioning the conjugate gradient algorithm