This paper is concerned with optimal boundary control of an instationary reaction-diffusion system in three spatial dimensions. This problem involves a coupled nonlinear system of parabolic differential equations with bilateral as well as integral control constraints. The integral constraint is included in the cost by a penalty term whereas the bilateral control constraints are handled explicit...

We consider a PDE system comprising compressible hydrodynamics, flux-limited diffusion radiation transport and chemical ionization kinetics in a cosmologicallyexpanding universe. Under an operator-split framework, the cosmological hydrodynamics equations are solved through the Piecewise Parabolic Method, as implemented in the Enzo community hydrodynamics code. The remainder of the model, compri...

A new optimization formulation for simulating multiphase flow in porous media is introduced. A locally mass-conservative, mixed finite-element method is employed for the spatial discretization. An unconditionally stable, fully-implicit time discretization is used and leads to a coupled system of nonlinear equations that must be solved at each time step. We reformulate this system as a least squ...

This paper represents numerical simulation of fluid-structure interaction (FSI) system involving an incompressible viscous fluid and a lightweight elastic structure. We follow a semi-implicit approach in which we implicitly couple the added-mass term (pressure stress) of the fluid to the structure, while other terms are coupled explicitly. This significantly reduces the computational cost of th...

We solve the ghost-gluon system of Yang-Mills theory using Graphics Processing Units (GPUs). Working in Landau gauge, we use the Dyson-Schwinger formalism for the mathematical description as this approach is well-suited to directly benefit from the computing power of the GPUs. With the help of a Chebyshev expansion for the dressing functions and a subsequent appliance of a Newton-Raphson method...

This article describes the use of the cell broadband engine as a high-performance platform for simulating the discharge of a lead acid battery to determine its state of health in an embedded application. The discharging of the battery is modelled as a twodimensional electrochemical process. The model equations are a set of coupled highly non-linear partial differential equations that evolve wit...

This contribution gives an overview about new procedures for the parameter identification for the material characterisation of rubber blends. They are based on a Newton-Raphson procedure and a genetic algorithm. As basis serves an experimental investigation of the viscous properties of rubber blends by means of a capillary-viscometer. Because of simultaneous consideration of wall slippage, temp...

A model coupling differential equations and a sequence of constrained optimization problems is proposed to simulate the evolution of a population of particles at equilibrium interacting through a common medium. The first order optimality conditions of the optimization problems relaxed with barrier functions are coupled with the differential equations into a system of differential-algebraic equa...

We present in this paper a fully implicit finite element method tailored for the numerical modeling of inextensible fluidic membranes in a surrounding Newtonian fluid. We consider a highly simplified version of the Canham-Helfrich model for phospholipid membranes, in which the bending force and spontaneous curvature are disregarded. The coupled problem is formulated in a fully Eulerian framewor...

In Karakazian and Nassif (2019), the non-linear space-time Hasegawa–Mima plasma equation is formulated as a coupled system of two linear PDEs, solution which pair (u,w), with w=(I−Δ)u. The first hyperbolic type second elliptic type. Variational frames for obtaining weak solutions to initial value problem periodic boundary conditions were also derived. more recent work et al. (2022), numerical a...