Related papers: Telescopic projective integration for kinetic equa…
We consider the development of high order asymptotic-preserving linear multistep methods for kinetic equations and related problems. The methods are first developed for BGK-like kinetic models and then extended to the case of the full…
In this work, we propose a numerical approach for simulations of large deformations of interfaces in a level set framework. To obtain a fast and viable numerical solution in both time and space, temporal discretization is based on the…
In this paper we present a multilevel projection-based iterative scheme for solving thermal radiative transfer problems that performs iteration cycles on the high-order Boltzmann transport equation (BTE) and low-order moment equations.…
We introduce a class of explicit exponential Rosenbrock methods for the time integration of large systems of stiff differential equations. Their application with respect to simulation tasks in the field of visual computing is discussed…
Segregated Runge-Kutta (SRK) schemes are time integration methods for the incompressible Navier-Stokes equations. In this approach, convection and diffusion can be independently treated either explicitly or implicitly, which in particular…
This paper deals with the problem of simulating dense dispersed systems composed by large numbers of particles undergoing ballistic aggregation. The most classical approaches for dealing with such problems are represented by the so-called…
We present a methodology for simulating dilute suspensions of particles settling under gravity, with the main purpose of overcoming limitations of triply periodic configurations, mainly the strong vertical correlation that hinders the study…
Simulations of biophysical systems inevitably include steps that correspond to time integrations of ordinary differential equations. These equations are often related to enzyme action in the synthesis and destruction of molecular species,…
The movement of many organisms can be described as a random walk at either or both the individual and population level. The rules for this random walk are based on complex biological processes and it may be difficult to develop a tractable,…
We propose a numerical approach, of the BGK kinetic type, that is able to approximate with a given, but arbitrary, order of accuracy the solution of linear and non-linear convection-diffusion type problems: scalar advection-diffusion,…
This note is devoted to a simple method for proving hypocoercivity of the solutions of a kinetic equation involving a linear time relaxation operator, i.e. the construction of an adapted Lyapunov functional satisfying a Gronwall-type…
Explicit step-truncation tensor methods have recently proven successful in integrating initial value problems for high-dimensional partial differential equations (PDEs). However, the combination of non-linearity and stiffness may introduce…
In this paper, we propose a general framework to design asymptotic preserving schemes for the Boltzmann kinetic kinetic and related equations. Numerically solving these equations are challenging due to the nonlinear stiff collision (source)…
In our previous work, numerical schemes for a simplified version of 3-wave kinetic equations, in which only the simple forward-cascade terms of the collision operators are kept, have been successfully designed, especially to capture the…
This paper explores an iterative coupling approach to solve linear thermo-poroelasticity problems, with its application as a high-fidelity discretization utilizing finite elements during the training of projection-based reduced order…
Most numerical methods for time integration use real time steps. Complex time steps provide an additional degree of freedom, as we can select the magnitude of the step in both the real and imaginary directions. By time stepping along…
The simulation of viscoelastic time-evolution problems described by a large number of internal variables and with a large spectrum of relaxation times requires high computational resources for their resolution. Furthermore, the internal…
The present paper deals with the problem of improving the efficiency of large scale turbulent flow simulations. The high-fidelity methods for modelling turbulent flows become available for a wider range of applications thanks to the…
Many astrophysical simulations involve extreme dynamic range of timescales around 'special points' in the domain (e.g. black holes, stars, planets, disks, galaxies, shocks, mixing interfaces), where processes on small scales couple strongly…
Many clustering applications in machine learning and data mining rely on solving metric-constrained optimization problems. These problems are characterized by $O(n^3)$ constraints that enforce triangle inequalities on distance variables…