Related papers: Virtual domain extension for imposing boundary con…
Sakurai et al. (J Comput Phys, 2019) presented a flux-based volume penalization (VP) approach for imposing inhomogeneous Neumann boundary conditions on embedded interfaces. The flux-based VP method modifies the diffusion coefficient of the…
Conditional domain generation is a good way to interactively control sample generation process of deep generative models. However, once a conditional generative model has been created, it is often expensive to allow it to adapt to new…
This work discusses the correct modeling of the fully nonlinear free surface boundary conditions to be prescribed in water waves flow simulations based on potential flow theory. The main goal of such a discussion is that of identifying a…
We consider the linearized and nonlinear stationary incompressible flow around rotating and translating body in the exterior domain B with Lipschitz boundary. We derive the pointwise estimates for the pressure in both cases. Moreover, we…
A common approach for the numerical simulation of wave propagation on a spatially unbounded domain is to truncate the domain via an artificial boundary, thus forming a finite computational domain with an outer boundary. Absorbing boundary…
Nonlocal models provide exceptional simulation fidelity for a broad spectrum of scientific and engineering applications. However, wider deployment of nonlocal models is hindered by several modeling and numerical challenges. Among those, we…
We propose methods that augment existing numerical schemes for the simulation of hyperbolic balance laws with Dirichlet boundary conditions to allow for the simulation of a broad class of differential algebraic conditions. Our approach is…
Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. Here, we explore the use of Neural Ordinary Differential Equations, a recently introduced family of…
In this paper, we propose two approaches to apply boundary conditions for bond-based peridynamic models. There has been in recent years a renewed interest in the class of so-called non-local models, which include peridynamic models, for the…
Stability and boundedness analysis for vector nonlinear systems with variable delays and coefficients remains challenging due to the conservatism of existing methods. Moreover, estimates of the transient behavior of solution norms remain…
We discuss artificial boundary conditions for stationary Navier-Stokes flows past bodies in the half-plane, for a range of low Reynolds numbers. When truncating the half-plane to a finite domain for numerical purposes, artificial boundaries…
Time-dependent wave equations represent an important class of partial differential equations (PDE) for describing wave propagation phenomena, which are often formulated over unbounded domains. Given a compactly supported initial condition,…
Control barrier functions (CBFs) are a popular tool for safety certification of nonlinear dynamical control systems. Recently, CBFs represented as neural networks have shown great promise due to their expressiveness and applicability to a…
We consider the numerical integration of Langevin equations for particles in a channel, in the presence of boundary conditions fixing the concentration values at the ends. This kind of boundary condition appears for instance when…
We study the simulation of charged systems in the presence of general boundary conditions in a local Monte Carlo algorithm based on a constrained electric field. We firstly show how to implement constant-potential, Dirichlet, boundary…
We explore how neural differential equations (NDEs) may be trained on highly resolved fluid-dynamical models of unresolved scales providing an ideal framework for data-driven parameterizations in climate models. NDEs overcome some of the…
We present an efficient and accurate immersed boundary (IB) finite element (FE) solver for numerically solving incompressible Navier--Stokes equations. Particular emphasis is given to internal flows with complex geometries (blood flow in…
Deep learning (DL) has demonstrated promise for accelerating and enhancing the accuracy of flow physics simulations, but progress is constrained by the scarcity of high-fidelity training data, which is costly to generate and inherently…
The precise simulation of turbulent flows is of immense importance in a variety of scientific and engineering fields, including climate science, freshwater science, and the development of energy-efficient manufacturing processes. Within the…
The goal of this work is to develop deep learning numerical methods for solving option XVA pricing problems given by non-linear PDE models. A novel strategy for the treatment of the boundary conditions is proposed, which allows to get rid…