Related papers: The Pencil Code, a modular MPI code for partial di…
Partial differential equations (PDEs) are crucial in modeling diverse phenomena across scientific disciplines, including seismic and medical imaging, computational fluid dynamics, image processing, and neural networks. Solving these PDEs at…
This paper examines aspirational requirements for software addressing mixed-integer optimization problems constrained by the nonlinear Shallow Water partial differential equations (PDEs), motivated by applications such as river-flow…
Differentiable programming allows for derivatives of functions implemented via computer code to be calculated automatically. These derivatives are calculated using automatic differentiation (AD). This thesis explores two applications of…
The new code for numerical simulation of magnetic hydrodynamical astrophysical flows with consideration of chemical reactions is given in the paper. At the heart of the code - the new original low-dissipation numerical method based on a…
Learning the full family of solutions to parameterized partial differential equations (PDEs) is a central challenge to our ability to model the behavior of heterogeneous systems, with a variety of fundamental and application-oriented…
Multiparticle collision dynamics (MPCD) is a flexible and robust mesoscale computational technique for simulating solvent-mediated hydrodynamic interactions in soft materials. Here, we provide a critical overview of the MPCD method and…
We describe pyro: a simple, freely-available code to aid students in learning the computational hydrodynamics methods widely used in astrophysics. pyro is written with simplicity and learning in mind and intended to allow students to…
Two methods for solid body representation in flow simulations available in the Pencil Code are the immersed boundary method and overset grids. These methods are quite different in terms of computational cost, flexibility and numerical…
Hybrid codes are widely used to model ion-scale phenomena in space plasmas. Hybrid codes differ from full particle (PIC) codes in that the electrons are modeled as a fluid that is usually assumed to be massless, while the electric field is…
Hybrid-VPIC is an extension of the open-source high-performance particle-in-cell (PIC) code VPIC incorporating hybrid kinetic ion/fluid electron solvers. This paper describes the models that are available in the code and gives an overview…
Multiparticle collision dynamics (MPCD) is a relatively new algorithm of fluid flow simulations that has been applied mostly to flows around simple objects. One might ask how it behaves in more complex flows. Therefore, we extend MPCD to…
Modeling multi-scale collisionless magnetized processes constitutes an important numerical challenge. By treating electrons as a fluid and ions kinetically, the so-called hybrid Particle-In-Cell (PIC) codes represent a promising…
We present a numerical scheme geared for high performance computation of wall-bounded turbulent flows. The number of all-to-all communications is decreased to only six instances by using a two-dimensional (pencil) domain decomposition and…
The pseudospectral method is a highly accurate numerical scheme suitable for turbulence simulations. We have developed an open-source pseudospectral code, \textsc{\textsf{Calliope}}, which adopts the P3DFFT library \citep{Pekurovsky2012} to…
Recent advances in high-resolution imaging techniques and particle-based simulation methods have enabled the precise microscopic characterization of collective dynamics in various biological and engineered active matter systems. In…
A two dimensional hydrochemical hybrid code, KM2, is constructed to deal with astrophysical problems that would require coupled hydrodynamical and chemical evolution. The code assumes axisymmetry in cylindrical coordinate system, and…
The field of partial differential equations (PDEs) is vast in size and diversity. The basic reason for this is that essentially all fundamental laws of physics are formulated in terms of PDEs. In addition, approximations to these…
In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…
Developers of Molecular Dynamics (MD) codes face significant challenges when adapting existing simulation packages to new hardware. In a continuously diversifying hardware landscape it becomes increasingly difficult for scientists to be…
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…