Related papers: Tuning symplectic integrators is easy and worthwhi…
This paper presents an analysis of the energy consumption of an extensive number of the optimisations a modern compiler can perform. Using GCC as a test case, we evaluate a set of ten carefully selected benchmarks for five different…
We examine the effect of numerical integration on the convergence of high order pyramidal finite element methods. Rational functions are indispensable to the construction of pyramidal interpolants so the conventional treatment of numerical…
We present new splitting methods designed for the numerical integration of near-integrable Hamiltonian systems, and in particular for planetary N-body problems, when one is interested in very accurate results over a large time span. We…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
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…
Integration by parts is used to reduce scalar Feynman integrals to master integrals.
We explore the combination of deterministic and Monte Carlo methods to facilitate efficient automatic numerical computation of multidimensional integrals with singular integrands. Two adaptive algorithms are presented that employ recursion…
Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical numerical solvers are typically employed to compute the…
Particle-In-Cell codes are widely used for plasma physics simulations. It is often the case that particles within a computational cell need to be split to improve the statistics or, in the case of non-uniform meshes, to avoid the…
The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the…
Many force-gradient explicit symplectic integration algorithms have been designed for the Hamiltonian $H=T (\mathbf{p})+V(\mathbf{q})$ with kinetic energy $T(\mathbf{p})=\mathbf{p}^2/2$ in the existing references. When the force-gradient…
Partition functions for non-interacting particles are known to be symmetric functions. It is shown that powerful group-theoretical techniques can be used not only to derive these relationships, but also to significantly simplify calculation…
We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…
Computing according to laymens procedures is changed to contain a paradigm of inoptimality in the high level and assembled code. The code is changed to maximize the flow of information contained in the electrons so that they function more…
Excellent computer simulations are done for a purpose. The most valid purposes are to explore uncharted territory, to resolve a well-posed scientific or technical question, or to make a design choice. Stand-alone modeling can serve the…
Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…
The goal of inductive logic programming is to induce a logic program (a set of logical rules) that generalises training examples. Inducing programs with many rules and literals is a major challenge. To tackle this challenge, we introduce an…
A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical…
We find that with uniform mesh, the numerical schemes derived from finite element method can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimentional case in certain discrete…
The polysymplectic analysis of the Short Pulse Equation known in nonlinear optics is used in order to construct a geometric polysymplectic integrator for it. The proposed scheme turns out to be much more effective than other standard…