Adaptivity with moving grids
In this article we survey r-adaptive (or moving grid) methods for solving time-dependent
partial differential equations (PDEs). Although these methods have received much less …
partial differential equations (PDEs). Although these methods have received much less …
[LIBRO][B] A concise introduction to geometric numerical integration
Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous
Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the …
Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the …
Backward error analysis for numerical integrators
S Reich - SIAM Journal on Numerical Analysis, 1999 - SIAM
Backward error analysis has become an important tool for understanding the long time
behavior of numerical integration methods. This is true in particular for the integration of …
behavior of numerical integration methods. This is true in particular for the integration of …
Understanding self-attention mechanism via dynamical system perspective
The self-attention mechanism (SAM) is widely used in various fields of artificial intelligence
and has successfully boosted the performance of different models. However, current …
and has successfully boosted the performance of different models. However, current …
Implementing few-body algorithmic regularization with post-Newtonian terms
S Mikkola, D Merritt - The Astronomical Journal, 2008 - iopscience.iop.org
We discuss the implementation of a new regular algorithm for simulation of the gravitational
few-body problem. The algorithm uses components from earlier methods, including the …
few-body problem. The algorithm uses components from earlier methods, including the …
Geometric integration and its applications
CJ Budd, MD Piggott - 2001 - ems.press
Geometric integration is the general term for a set of numerical algorithms for solving
differential equations that aim to reproduce qualitative features in the solution. These can be …
differential equations that aim to reproduce qualitative features in the solution. These can be …
A class of symplectic integrators with adaptive time step for separable Hamiltonian systems
M Preto, S Tremaine - The Astronomical Journal, 1999 - iopscience.iop.org
Symplectic integration algorithms are well suited for long-term integrations of Hamiltonian
systems, because they preserve the geometric structure of the Hamiltonian flow. However …
systems, because they preserve the geometric structure of the Hamiltonian flow. However …
Symplectic local time-step** in non-dissipative DGTD methods applied to wave propagation problems
S Piperno - ESAIM: Mathematical Modelling and Numerical …, 2006 - numdam.org
The Discontinuous Galerkin Time Domain (DGTD) methods are now popular for the solution
of wave propagation problems. Able to deal with unstructured, possibly locally-refined …
of wave propagation problems. Able to deal with unstructured, possibly locally-refined …
On fast simulation of dynamical system with neural vector enhanced numerical solver
The large-scale simulation of dynamical systems is critical in numerous scientific and
engineering disciplines. However, traditional numerical solvers are limited by the choice of …
engineering disciplines. However, traditional numerical solvers are limited by the choice of …
Variable time step integration with symplectic methods
E Hairer - Applied Numerical Mathematics, 1997 - Elsevier
Symplectic methods for Hamiltonian systems are known to have favorable properties
concerning long-time integrations (no secular terms in the error of the energy integral, linear …
concerning long-time integrations (no secular terms in the error of the energy integral, linear …