Related papers: Hermite integrator for high-order mesh-free scheme…
The dynamic behavior of jointed assemblies exhibiting friction nonlinearities features amplitude-dependent dissipation and stiffness. To develop numerical simulations for predictive and design purposes, macro-scale High Fidelity Models…
Mesh-free numerical methods offer flexibility in discretising complex geometries, showing potential where mesh-based methods struggle. While high-order approximations can be obtained via consistency correction using linear systems, they…
Symplectic schemes are powerful methods for numerically integrating Hamiltonian systems, and their long-term accuracy and fidelity have been proved both theoretically and numerically. However direct applications of standard symplectic…
We propose a method of construction of a cubic interaction in massless Higher Spin gauge theory both in flat and in AdS space-times of arbitrary dimensions. We consider a triplet formulation of the Higher Spin gauge theory and generalize…
Balsara (2001) showed the importance of divergence-free reconstruction in adaptive mesh refinement problems for magnetohydrodynamics (MHD) and the importance of the same for designing robust second order schemes for MHD was shown in Balsara…
We derive a novel computational scheme for functional Renormalization Group (fRG) calculations for interacting fermions on 2D lattices. The scheme is based on the exchange parametrization fRG for the two-fermion interaction, with additional…
In this paper we propose an efficient third-order numerical scheme for backward stochastic differential equations(BSDEs). We use 3-point Gauss-Hermite quadrature rule for approximation of the conditional expectation and avoid spatial…
We present two new Lagrangian methods for hydrodynamics, in a systematic comparison with moving-mesh, SPH, and stationary (non-moving) grid methods. The new methods are designed to simultaneously capture advantages of both smoothed-particle…
The nonlinear gyrokinetic equations describe plasma turbulence in laboratory and astrophysical plasmas. To solve these equations, massively parallel codes have been developed and run on present-day supercomputers. This paper describes…
Contour integration schemes are a valuable tool for the solution of difficult interior eigenvalue problems. However, the solution of many large linear systems with multiple right hand sides may prove a prohibitive computational expense. The…
Multiderivative time integrators have a long history of development for ordinary differential equations, and yet to date, only a small subset of these methods have been explored as a tool for solving partial differential equations (PDEs).…
We develop new numerical schemes for Vlasov--Poisson equations with high-order accuracy. Our methods are based on a spatially monotonicity-preserving (MP) scheme and are modified suitably so that positivity of the distribution function is…
In this work, the benefits of the phase fitting technique are embedded in high order discrete Lagrangian integrators. The proposed methodology creates integrators with zero phase lag in a test Lagrangian in a similar way used in phase…
Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it…
Deriving analytical solutions of ordinary differential equations is usually restricted to a small subset of problems and numerical techniques are considered. Inevitably, a numerical simulation of a differential equation will then always be…
In the numerical solution of partial differential equations using a method-of-lines approach, the availability of high order spatial discretization schemes motivates the development of sophisticated high order time integration methods. For…
Magnetic quadrupoles are essential components of particle accelerators like the Large Hadron Collider. In order to study numerically the stability of the particle beam crossing a quadrupole, a large number of particle revolutions in the…
To achieve efficient and accurate long-time integration, we propose a fast, accurate, and stable high-order numerical method for solving fractional-in-space reaction-diffusion equations. The proposed method is explicit in nature and…
We introduce a class of general purpose linear multisymplectic integrators for Hamiltonian wave equations based on a diamond-shaped mesh. On each diamond, the PDE is discretized by a symplectic Runge--Kutta method. The scheme advances in…
Finite element discretization of time dependent problems also require effective time-stepping schemes. While implicit Runge-Kutta methods provide favorable accuracy and stability problems, they give rise to large and complicated systems of…