Critical time-step size analysis and mass scaling by ghost-penalty for immersogeometric explicit dynamics

In this article, we study the effect of small-cut elements on the critical time-step size in an immersogeometric explicit dynamics context. We analyze different formulations for second-order (membrane) and fourth-order (shell-type) equations, and derive scaling relations between the critical time-step size and the cut-element size for various...

Towards parallel time-stepping for the numerical simulation of atherosclerotic plaque growth

The numerical simulation of atherosclerotic plaque growth is computationally prohibitive, since it involves a complex cardiovascular fluid-structure interaction (FSI) problem with a characteristic time scale of milliseconds to seconds, as well as a plaque growth process governed by reaction-diffusion equations, which takes place over several...

The Seven-League Scheme: Deep Learning for Large Time Step Monte Carlo Simulations of Stochastic Differential Equations

We propose an accurate data-driven numerical scheme to solve stochastic differential equations (SDEs), by taking large time steps. The SDE discretization is built up by means of the polynomial chaos expansion method, on the basis of accurately determined stochastic collocation (SC) points. By employing an artificial neural network to learn these...

Adaptive multilevel space-time-stepping scheme for transport in heterogeneous porous media (ADM-LTS)

We present ADM-LTS, an adaptive multilevel space-time-stepping scheme for transport in heterogeneous porous media. At each time step, firstly, the flow (pressure) solution is obtained. Then, the transport equation is solved using the ADM-LTS method, which consists of two stages. In the first stage, an initial solution is obtained by imposing the...

Biomedical implications from mathematical models for the simulation of dermal wound healing

Dermal wounds are a significant global problem; although the treatment of these wounds has improved considerably over the last few decades, a treatment still does not result in a complete regeneration of the injured tissue. Instead, the final outcome of the healing process is scar tissue. The material properties of scar tissue are different from...

Effect of time stepping strategy on adjoint-based production optimization

The adjoint gradient method is well recognized for its efficiency in large-scale production optimization. When implemented in a sequential quadratic programming (SQP) algorithm, adjoint gradients enable the construction of a quadratic approximation of the objective function and linear approximation of the nonlinear constraints using just one...

Time Dependent Flow Simulations using the Least Squares Spectral Element Method with Direct Minimization

In this work a new approach to time dependent problems in combination with the Least-Squares Spectral Element Method (LSQSEM) will be discussed. Various timestepping formulations will be presented. These time-stepping formulations will be compared to the full space-time formulation. It will be shown that time-stepping formulations give accurate...

Time Dependent Flow Simulations using the Least Squares Spectral Element Method with Direct Minimization

In this work a new approach to time dependent problems in combination with the Least-Squares Spectral Element Method (LSQSEM) will be discussed. Various time-stepping formulations will be presented. These time-stepping formulations will be compared to the full space-time formulation. It will be shown that time-stepping formulations give accurate...