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Lagrangian particle-based methods have opened new perspectives for the investigation of complex problems with large free-surface deformation. Some well-known particle-based methods adopted to solve non-linear hydrodynamics problems are the…
Stochastic nonlinear dynamical systems can undergo rapid transitions relative to the change in their forcing, for example due to the occurrence of multiple equilibrium solutions for a specific interval of parameters. In this paper, we…
We introduce a novel artificial compressibility technique to approximate the incompressible Navier-Stokes equations with variable fluid properties such as density and dynamical viscosity. The proposed scheme used the couple pressure and…
The standard smoothed particle hydrodynamics (SPH) method suffers from tensile instability, resulting in particle clumping and void regions under negative pressure conditions. In this study, we extend the transport-velocity formulation of…
Studying compact star binaries and their mergers is integral to determining progenitors for observable transients. Today, compact-star mergers are typically studied via state-of-the-art computational fluid dynamics codes. One such numerical…
Stochastic algorithms are efficient approaches to solving machine learning and optimization problems. In this paper, we propose a general framework called Splash for parallelizing stochastic algorithms on multi-node distributed systems.…
In this paper, we propose a stochastic scheduling strategy for estimating the states of N discrete-time linear time invariant (DTLTI) dynamic systems, where only one system can be observed by the sensor at each time instant due to practical…
In this paper, we propose multicontinuum splitting schemes for multiscale problems, focusing on a parabolic equation with a high-contrast coefficient. Using the framework of multicontinuum homogenization, we introduce spatially smooth…
A new variational inference method, SPH-ParVI, based on smoothed particle hydrodynamics (SPH), is proposed for sampling partially known densities (e.g. up to a constant) or sampling using gradients. SPH-ParVI simulates the flow of a fluid…
The splitting method is a powerful method for solving partial differential equations. Various splitting methods have been designed to separate different physics, nonlinearities, and so on. Recently, a new splitting approach has been…
In this paper we present an extension of standard iterative splitting schemes to multiple splitting schemes for solving higher order differential equations. We are motivated by dynamical systems, which occur in dynamics of the electrons in…
To tackle the difficulties faced by both stochastic dynamic programming and scenario tree methods, we present some variational approach for numerical solution of stochastic optimal control problems. We consider two different interpretations…
In this paper, we introduce a technique to enhance the computational efficiency of solution algorithms for high-dimensional discrete simulation-based optimization problems. The technique is based on innovative adaptive partitioning…
Particle methods are less computationally efficient than grid based numerical solution of the Navier Stokes equation. However, they have important advantages including rigorous mass conservation, momentum conservation and isotropy. In…
We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. Via expanding the phase space to include time $t$, we give a more general…
A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is…
We introduce a new discretization of a mixed formulation of the incompressible Stokes equations that includes symmetric viscous stresses. The method is built upon a mass conserving mixed formulation that we recently studied. The improvement…
Deterministic simulations of the rate equations governing cluster dynamics in materials are limited by the number of equations to integrate. Stochastic simulations are limited by the high frequency of certain events. We propose a coupling…
A new approach for integration of motion in many-body systems of interacting polyatomic molecules is proposed. It is based on splitting time propagation of pseudo-variables in a modified phase space, while the real translational and…
Graphics research on Smoothed Particle Hydrodynamics (SPH) has produced fantastic visual results that are unique across the board of research communities concerned with SPH simulations. Generally, the SPH formalism serves as a spatial…