Related papers: Projective Integration Schemes for Hyperbolic Mome…
This paper presents a new method for modelling periodic signals having an aperiodic trend, using the method of variable projection. It is a major extension to the IEEE-standard 1057 by permitting the background to be time varying;…
This work is aimed to develop a new class of methods for the BGK model of the Boltzmann equation. This technique allows to get high order of accuracy both in space and time, theoretically without CFL stability limitation. It's based on a…
Simulations of the dynamics generated by partial differential equations (PDEs) provide approximate, numerical solutions to initial value problems. Such simulations are ubiquitous in scientific computing, but the correctness of the results…
For simulating incompressible flows by projection methods. it is generally accepted that the pressure-correction stage is the most time-consuming part of the flow solver. The objective of the present work is to develop a fast hybrid…
We have developed a new, very efficient numerical scheme to solve the CR diffusion convection equation that can be applied to the study of the nonlinear time evolution of CR modified shocks for arbitrary spatial diffusion properties. The…
We propose an iterative solution method for the 3D high-frequency Helmholtz equation that exploits a contour integral formulation of spectral projectors. In this framework, the solution in certain invariant subspaces is approximated by…
Linear models for the radiative transfer equation have been well developed, while nonlinear models are seldom investigated even for slab geometry due to some essential difficulties. We have proposed a moment model in MPN for slab geometry…
Projection predictive inference is a decision theoretic Bayesian approach that decouples model estimation from decision making. Given a reference model previously built including all variables present in the data, projection predictive…
The numerical simulation of incompressible flows is challenging due to the tight coupling of velocity and pressure. Projection methods offer an effective solution by decoupling these variables, making them suitable for large-scale…
Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…
Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…
To obtain explicit understanding of the behavior of dynamical systems, geometrical methods and slow-fast analysis have proved to be highly useful. Such methods are standard for smooth dynamical systems, and increasingly used for continuous,…
Fully implicit timestepping methods have several potential advantages for atmosphere/ocean simulation. First, being unconditionally stable, they degrade more gracefully as the Courant number increases, typically requiring more solver…
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…
This paper introduces a continuous-time constrained nonlinear control scheme which implements a model predictive control strategy as a continuous-time dynamic system. The approach is based on the idea that the solution of the optimal…
We apply moment methods to obtaining an approximate analytical solution to Knudsen layers. Based on the hyperbolic regularized moment system for the Boltzmann equation with the Shakhov collision model, we derive a linearized hyperbolic…
Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques…
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…
We present a fully pseudo-spectral scheme to solve axisymmetric hyperbolic equations of second order. With the Chebyshev polynomials as basis functions, the numerical grid is based on the Lobbato (for two spatial directions) and Radau (for…
The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that…