We show how the software Comsol Multiphysics can be used to solve PDE-constrained optimal control problems. We give a general formulation for such kind of problems and derive the adjoint equation and optimality system. Then these preliminaries are specified for the stationary Navier-Stokes equations with distributed and boundary control. The main steps to define and solve a PDE with Comsol Mult...

Droplet impact onto a solid surface is modeled and numerically simulated using an ALE formulation of the Navier-Stokes free surface equations. The triple line dynamics aspect is modeled implicitely through the Shikhmurzaev theory. Those equations involve a generalized Navier slip boundary conditions with the variation of the surface tension near the triple line (thus a local Marangoni effect). ...

Droplet impact onto a solid surface is modeled and numerically simulated using an ALE formulation of the Navier-Stokes free surface equations. The triple line dynamics aspect is modeled implicitely through the Shikhmurzaev theory. Those equations involve a generalized Navier slip boundary conditions with the variation of the surface tension near the triple line (thus a local Marangoni effect). ...

While Comsol Multiphysics has great flexibility for modeling photonic devices, the computational demands of the general finite element method make it most suitable for small devices, on the order of a few microns in extent. Many integrated optical devices are much larger, having lengths of hundreds of microns or millimeters. A beam propagation method (BPM), which applies some simplifying assump...

In this paper, analytical and numerical methods for simulating squeeze-film air damping affecting suspended and perforated movable micro-surfaces are analyzed. Numerical solutions are obtained by full 3-D Navier-Stokes numerical analysis, carried out by a commercial finite element code, COMSOL Multiphysics, and are compared with those obtained using different analytical models proposed in liter...

in this paper, the capabilities of modeling linear viscoelasticty in a finite element method software package (comsol multiphysics) have been investigated. the governing equations of linear viscoelasticity have been developed for 2d cases of plane stress and plane strain. these equations have been verified by solving a related engineering example. since the developed equations are suitable for ...

Mastery of finite element theory is necessary to write finite element program, but it is not necessary to use COMSOL Multiphysics package. It is only necessary to understand the physical problem at hand, how to use the finite element program, and how to interpret the results. This paper gives an introduction to modeling in COMSOL Multiphysics, as being employed in the course heat transfer, by d...

Proportional solenoids are wellknown and used in a wide range of applications today. However, the theory behind the functional principle of proportional magnetic actuators is not very well represented in literature. This paper discusses methods of influencing the characteristic force-strokecurves of magnetic actuators by means of different pole geometries. The conical design of the stator pole,...