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Semi-implicit methods are powerful and efficient tools for the three-dimensional modeling of coastal and oceanic processes. A semi-implicit finite difference method for 3D hydrostatic primitive equations is presented in this paper. The…
In this paper we propose an explicit two-level conservative scheme based on a TE/TM like splitting of the field components in time. Its dispersion properties are adjusted to accelerator problems. It is simpler and faster than the implicit…
In this paper, we propose an efficient exponential integrator finite element method for solving a class of semilinear parabolic equations in rectangular domains. The proposed method first performs the spatial discretization of the model…
In this article we present a novel staggered semi-implicit hybrid finite-volume/finite-element (FV/FE) method for the resolution of weakly compressible flows in two and three space dimensions. The pressure-based methodology introduced in…
We present an implicit Split-Step explicit Euler type Method (dubbed SSM) for the simulation of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) with drifts of superlinear growth in space, Lipschitz in measure and non-constant…
We develop a semi-implicit algorithm for time-accurate simulation of the compressible Navier-Stokes equations, with special reference to wall-bounded flows. The method is based on linearization of the partial convective fluxes associated…
We develop a diffuse-interface continuum model for membrane electroporation that couples a phase field for pore geometry to a quasi-static electrolyte potential and a spatially varying leaky-dielectric model for the transmembrane voltage.…
The quest for analytical solutions to differential equations has traditionally been constrained by the need for extensive mathematical expertise. Machine learning methods like genetic algorithms have shown promise in this domain, but are…
We present a full-vector finite element method (FEM) mode solver for dielectric waveguides based on a mixed Nedelec-Lagrange discretization of Maxwell's curl equations in the frequency domain. The formulation combines edge elements for…
This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of partial differential equations. As opposed to the existing…
In this paper we combine a flexible covariant formulation of the shallow water equations with the semi-implicit numerical scheme developed over the years by Casulli and collaborators. After adopting an orthogonal, but non-orthonormal,…
Typical areas of application of explicit dynamics are impact, crash test, and most importantly, wave propagation simulations. Due to the numerically highly demanding nature of these problems, efficient automatic mesh generators and…
This study introduces a first step for constructing a hybrid reduced-order models (ROMs) for segregated fluid-structure interaction in an Arbitrary Lagrangian-Eulerian (ALE) approach at a high Reynolds number using the Finite Volume Method…
While autoregressive machine-learning-based emulators have been trained to produce stable and accurate rollouts in the climate of the present-day and recent past, none so far have been trained to emulate the sensitivity of climate to…
In this paper, a type of novel projection-based, time-segmented reduced order model (ROM) is proposed for dynamic fluid-structure interaction (FSI) problems based upon the arbitrary Lagrangian--Eulerian (ALE)-finite element method (FEM) in…
We implemented the pressure-implicit with splitting of operators (PISO) and semi-implicit method for pressure-linked equations (SIMPLE) solvers of the Navier-Stokes equations on Fermi-class graphics processing units (GPUs) using the CUDA…
A new flow solver scalable on multiple Graphics Processing Units (GPUs) for direct numerical simulation of wall-bounded incompressible flow is presented. This solver utilizes a previously reported work (J. Comp. Physics, vol. 352 (2018),…
A rigid body model for the dynamics of a marine vessel, used in simulations of offshore pipe-lay operations, gives rise to a set of ordinary differential equations with controls. The system is input-output passive. We propose…
An Integral Equation (IE) based field solver to compute the scattered fields from spatially dispersive metasurfaces is proposed and numerically confirmed using various examples involving physical unit cells. The work is a continuation of…
Recently a splitting approach has been presented for the simulation of sonic-boom propagation. Splitting methods allow one to divide complicated partial differential equations into simpler parts that are solved by specifically tailored…