Related papers: Geometric Methods for Adjoint Systems
We apply the concept of Asymptotic Preserving (AP) schemes to the linearized p-system and discretize the resulting elliptic equation using standard continuous Finite Elements instead of Finite Differences. The fully discrete method is…
Hamiltonian systems of ordinary and partial differential equations are fundamental mathematical models spanning virtually all physical scales. A critical property for the robustness and stability of computational methods in such systems is…
An adjoint-based shape optimization method for solid bodies subjected to both rarefied and continuum gas flows is proposed. The gas-kinetic BGK equation with the diffuse-reflection boundary condition is used to describe the multiscale gas…
In this paper, we develop a structure-preserving discretization of the Lagrangian framework for electromagnetism, combining techniques from variational integrators and discrete differential forms. This leads to a general family of…
There is a growing interest in the conservation of invariants when numerically solving a system of ordinary differential equations. Methods that exactly preserve these quantities in time are known as geometric integrators. In this paper we…
We present and discuss three discontinuous Galerkin (dG) discretizations for the anisotropic heat conduction equation on non-aligned cylindrical grids. Our most favourable scheme relies on a self-adjoint local dG (LDG) discretization of the…
We develop a numerical solver for three-dimensional wave propagation in coupled poroelastic-elastic media, based on a high-order discontinuous Galerkin (DG) method, with the Biot poroelastic wave equation formulated as a first order…
By the simple finite element method, we study the symplectic, multisymplectic structures and relevant preserving properties in some semi-linear elliptic boundary value problem in one-dimensional and two-dimensional spaces respectively. We…
The adjoint method allows efficient calculation of the gradient with respect to the design variables of a topology optimization problem. This method is almost exclusively used in combination with traditional Finite-Element-Analysis, whereas…
We analyze composition methods with complex coefficients exhibiting the so-called ``symmetry-conjugate'' pattern in their distribution. In particular, we study their behavior with respect to preservation of qualitative properties when…
Geometric optics is analysed using the techniques of Presymplectic Geometry. We obtain the symplectic structure of the space of light rays in a medium of a non constant refractive index by reduction from a presymplectic structure, and using…
In this paper we introduce a procedure, based on the method of equivariant moving frames, for formulating continuous Galerkin finite element schemes that preserve the Lie point symmetries of initial value problems for ordinary differential…
We present an adjoint-based optimization method to invert for stress and frictional parameters used in earthquake modeling. The forward problem is linear elastodynamics with nonlinear rate-and-state frictional faults. The misfit functional…
Discrete variational methods show excellent performance in numerical simulations of mechanical systems. In this paper, we adapt discrete variational integrators for the case of mechanical systems with double-bracket dissipation. In…
Classical energy-momentum methods study the existence and stability properties of solutions of $t$-dependent Hamilton equations on symplectic manifolds whose evolution is given by their Hamiltonian Lie symmetries. The points of such…
The sharp increasing in fabrication capabilities of nanomaterials, and complex structures such as meta-surfaces and metalens, has opened to the possibility of employing them for accurately control the electromagnetic field, beyond the…
Many differential equations with physical backgrounds are described as gradient systems, which are evolution equations driven by the gradient of some functionals, and such problems have energy conservation or dissipation properties. For…
We consider structure-preserving methods for conservative systems, which rigorously replicate the conservation property yielding better numerical solutions. There, corresponding to the skew-symmetry of the differential operator, that of…
Symplectic integration of autonomous Hamiltonian systems is a well-known field of study in geometric numerical integration, but for non-autonomous systems the situation is less clear, since symplectic structure requires an even number of…
A port-Hamiltonian (pH) system formulation is a geometrical notion used to formulate conservation laws for various physical systems. The distributed parameter port-Hamiltonian formulation models infinite dimensional Hamiltonian dynamical…