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Parallel multiphysics simulations often suffer from load imbalances originating from the applied coupling of algorithms with spatially and temporally varying workloads. It is thus desirable to minimize these imbalances to reduce the time to…
This paper studies the performative prediction problem where a learner aims to minimize the expected loss with a decision-dependent data distribution. Such setting is motivated when outcomes can be affected by the prediction model, e.g., in…
We present an ``equation-free'' multiscale approach to the simulation of unsteady diffusion in a random medium. The diffusivity of the medium is modeled as a random field with short correlation length, and the governing equations are cast…
In the present article, an approach to find the exact solution of the fractional Fokker-Planck equation is presented. It is based on transforming it to a system of first-order partial differential equation via Hopf transformation, together…
A fractional relaxation equation in dielectrics with response function of the Havriliak-Negami type is derived. An explicit expression for the fractional operator in this equation is obtained and Monte Carlo algorithm for calculation of…
This paper proposes a thermodynamically consistent phase-field damage model for viscoelastic materials. Suitable free-energy and pseudo-potentials of dissipation are developed to build a model leading to a stress-strain relation, under the…
Nonlinear PDEs give rise to complex dynamics that are often difficult to analyze in state space due to their relatively large numbers of degrees of freedom, ill-conditioned operators, and changing spatial and parameter resolution…
This study extends the use of symbolic computation in Matrix Structural Analysis (MSA) to plane (2D) trusses, building on previous work that focused on continuous beams. An open-source MATLAB program, hosted on GitHub, was developed to…
We present Decapodes, a diagrammatic tool for representing, composing, and solving partial differential equations. Decapodes provides an intuitive diagrammatic representation of the relationships between variables in a system of equations,…
Macroscopic models which distinguish the longitudinal and transverse temperatures can provide improved descriptions of the microscopic shock structures as revealed by molecular dynamics simulations. Additionally, we can include three…
In this paper, the partial relaxation approach is introduced and applied to DOA estimation using spectral search. Unlike existing methods like Capon or MUSIC which can be considered as single source approximations of multi-source estimation…
A novel approach called Moate Simulation is presented to provide an accurate numerical evolution of probability distribution functions represented on grids arising from stochastic differential processes where initial conditions are…
Fractional derivative relaxation type equations (FREs) including fractional diffusion equation and fractional relaxation equation, have been widely used to describe anomalous phenomena in physics. To utilize the characteristics of…
This article presents new numerical simulation tools, respectively developed in Matlab and Blender softwares. Available in open-source under the GPL 3.0 license, it uses a ray-tracing/image-sources hybrid method to calculate the room…
A new approach to calculate the vibrational distribution function of molecules in a medium providing energy for vibrational excitation is proposed and demonstrated. The approach is an improvement of solution methods based on the…
The solution of the classic problem of stress in a rotating elastic disk or cylinder, as solved in standard texts on elasticity theory, has two features: dynamical equations are used that are valid only in an inertial frame of reference,…
We present an efficient computational methodology to obtain the viscoelastic response of dilute solutions of semiflexible filaments. By considering an approach based on the fluctuation-dissipation theorem, we were able to evaluate the…
In this paper, we develop and analyze a stochastic algorithm for solving space-time fractional diffusion models, which are widely used to describe anomalous diffusion dynamics. These models pose substantial numerical challenges due to the…
Simulating physical problems involving multi-time scale coupling is challenging due to the need of solving these multi-time scale processes simultaneously. In response to this challenge, this paper proposed an explicit multi-time step…
In this paper, we propose a variable time-step linear relaxation scheme for time-fractional phase-field equations with a free energy density in general polynomial form. The $L1^{+}$-CN formula is used to discretize the fractional…