相关论文: Antisymmetry, pseudospectral methods, and conserva…
In this paper, we prove necessary and sufficient conditions for a hybridizable discontinuous Galerkin (HDG) method to satisfy a multisymplectic conservation law, when applied to a canonical Hamiltonian system of partial differential…
Many modern discontinuous Galerkin (DG) methods for conservation laws make use of summation by parts operators and flux differencing to achieve kinetic energy preservation or entropy stability. While these techniques increase the robustness…
This paper introduces general methodologies for constructing closed-form solutions to linear constant-coefficient partial differential equations (PDEs) with polynomial right-hand sides in two and three spatial dimensions. Polynomial…
Finite element simulations have been used to solve various partial differential equations (PDEs) that model physical, chemical, and biological phenomena. The resulting discretized solutions to PDEs often do not satisfy requisite physical…
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…
A new exponentially fitted version of the Discrete Variational Derivative method for the efficient solution of oscillatory complex Hamiltonian Partial Differential Equations is proposed. When applied to the nonlinear Schroedinger equation,…
Energy methods for constructing time-stepping algorithms are of increased interest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system energy. Alternatively, symplectic…
We propose a class of conservative discontinuous Galerkin methods for the Vlasov-Poisson system written as a hyperbolic system using Hermite polynomials in the velocity variable. These schemes are designed to be systematically as accurate…
A novel class of explicit high-order energy-preserving methods are proposed for general Hamiltonian partial differential equations with non-canonical structure matrix. When the energy is not quadratic, it is firstly done that the original…
In this contribution, we extend the hybridization framework for the Hodge Laplacian [Awanou et al., Hybridization and postprocessing in finite element exterior calculus, 2023] to port-Hamiltonian systems describing linear wave propagation…
This work discusses the model reduction problem for large-scale multi-symplectic PDEs with cubic invariants. For this, we present a linearly implicit global energy-preserving method to construct reduced-order models. This allows to…
New families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into three parts in such a…
This paper is concerned with developing and analyzing two novel implicit temporal discretization methods for the stochastic semilinear wave equations with multiplicative noise. The proposed methods are natural extensions of well-known…
Reduced basis methods are popular for approximately solving large and complex systems of differential equations. However, conventional reduced basis methods do not generally preserve conservation laws and symmetries of the full order model.…
In this paper, we propose an adaptive high-order method for hyperbolic systems of conservation laws. The proposed method is based on a dual formulation approach: Two numerical solutions, corresponding to conservative and nonconservative…
We propose energy-conserving discontinuous Galerkin (DG) methods for symmetric linear hyperbolic systems on general unstructured meshes. Optimal a priori error estimates of order $k+1$ are obtained for the semi-discrete scheme in one…
We present a brief overview of the different domain and space decomposition techniques that enter in developing and analyzing solvers for discontinuous Galerkin methods. Emphasis is given to the novel and distinct features that arise when…
Energy-preserving numerical methods for solving the Hodge wave equation is developed in this paper. Based on the de Rham complex, the Hodge wave equation can be formulated as a first-order system and mixed finite element methods using…
We analyze Galerkin discretizations of a new well-posed mixed space-time variational formulation of parabolic PDEs. For suitable pairs of finite element trial spaces, the resulting Galerkin operators are shown to be uniformly stable. The…
This work presents new parallelizable numerical schemes for the integration of Dissipative Particle Dynamics with Energy conservation (DPDE). So far, no numerical scheme introduced in the literature is able to correctly preserve the energy…