相关论文: FANTASY: User-Friendly Symplectic Geodesic Integra…

By combining a standard symmetric, symplectic integrator with a new step size controller, we provide an integration scheme that is symmetric, reversible and conserves the values of the constants of motion. This new scheme is appropriate for…

Most numerical integration algorithms are not designed specifically for Hamiltonian systems and do not respect their characteristic properties, which include the preservation of phase space volume with time. This can lead to spurious…

Symplectic integrator plays a pivotal role in the long-term tracking of charged particles within accelerators. To get symplectic maps in accurate simulation of single-particle trajectories, two key components are addressed: precise…

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…

We describe a technique for constructing a symplectic transfer map for a charged particle moving through an accelerator component with arbitrary three-dimensional static magnetic field. The transfer map is constructed by symplectic…

The real symplectic Stiefel manifold is the manifold of symplectic bases of symplectic subspaces of a fixed dimension. It features in a large variety of applications in physics and engineering. In this work, we study this manifold with the…

In today's modern wide-field galaxy surveys, there is the necessity for parametric surface brightness decomposition codes characterised by accuracy, small degree of user intervention, and high degree of parallelisation. We try to address…

In this project, we introduce OPESCI-FD, a Python package built on symbolic mathematics to automatically generate Finite Difference models from a high-level description of the model equations. We investigate applying this framework to…

We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the…

Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…

Plane Geometry Diagram Synthesis has been a crucial task in computer graphics, with applications ranging from educational tools to AI-driven mathematical reasoning. Traditionally, we rely on manual tools (e.g., Matplotlib and GeoGebra) to…

We implement and investigate the numerical properties of a new family of integrators connecting both variants of the symplectic Euler schemes, and including an alternative to the classical symplectic mid-point scheme, with some additional…

3D Gaussian Splatting (3DGS) has recently gained popularity as a faster alternative to Neural Radiance Fields (NeRFs) in 3D reconstruction and view synthesis methods. Leveraging the spatial information encoded in 3DGS, this work proposes…

In this paper, we introduce Pysimfrac, a open-source python library for generating 3-D synthetic fracture realizations, integrating with fluid simulators, and performing analysis. Pysimfrac allows the user to specify one of three fracture…

Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term…

Partial differential equations describing the dynamics of physical systems rarely have closed-form solutions. Fourier spectral methods, which use Fast Fourier Transforms (FFTs) to approximate solutions, are a common approach to solving…

We describe a parallel hybrid symplectic integrator for planetary system integration that runs on a graphics processing unit (GPU). The integrator identifies close approaches between particles and switches from symplectic to Hermite…

Fanpy is a free and open-source Python library for developing and testing multideterminant wavefunctions and related ab initio methods in electronic structure theory. The main use of Fanpy is to quickly prototype new methods by making it…

In the paper a recent enhancement to the open source package SfePy (Simple Finite Elements in Python, http://sfepy.org) is introduced, namely the addition of another numerical discretization scheme, the isogeometric analysis, to the…

In this paper, explicit stable integrators based on symplectic and contact geometries are proposed for a non-autonomous ordinarily differential equation (ODE) found in improving convergence rate of Nesterov's accelerated gradient method.…