Software packages COMSOL

In this work, the commercial software package Comsol Multiphysics 3.2 (Corn-sol AB, Stockholm, Sweden) was used to solve the system of nonlinear partial differential equations. Apart from predefined built-in applications, this tool enables the user to define and solve PDE systems by finite-element discretization. Taking advantage of the axial symmetry of the problem, the model domain can be simplified to two dimensions. In this domain, a structured quadrilateral mesh... 

Due to difficulty in implementing FEMs, commercial software packages like Comsol Multiphysics are often used, since they allow the application of these methods without implementing an in-house finite element code. Specific details of the working and potentialities of Comsol Multiphysics can be found in the programme manuals [6, 7],... 

To validate the used direct- and reverse models, additionally to fitting the experimental data to theoretical (Dodd-Deeds etc) models, also a FEM simulation of the measurement setup (coil above the metal plate) has been done for RRl-3 coil above metal2 (Nordic gold). COMSOL multiphysics-FEM simulation software package has been sued for such simulation. Got by COMSOL impedance results were used as input to the reverse model of Dodd-Deeds etc, and the results (Fig. 16) show the good correspondence of the models. 

For a sufficiently fine subdivision of the body, it is possible to find a suitably exact solution of the heat conduction problem. Several FEM software packages are available on the market. The ANSYS and the COMSOL systems are often used by calorimeter-developing corporations. The software can be used to define the time-dependent heat flux curves at any site of the calorimeter system and also to indicate the temperature field if this is necessary for the purposes of the discussion and for a better understanding including heat leaks of all kinds. 

The IDA generator-collector system has been simulated using the Laasonen (BI) scheme [374], explicit FD [375, 376], hopscotch and conformal mapping [220], the finite analytic numerical method [152], extrapolation using expanding space intervals [332] and ADI with expanding space intervals [348, 377]. Commercial FEM software packages Flux-Expert [324] and COMSOL Multiphysics [378] have also been employed. 

The numerical solutions of the governing model equations have been obtained (Ye et al., 2006 Abdullah et al., 2006) using the software package FEMLAB (Comsol, Sweden). The base values of model parameters were taken from the experimental work of Ye et al. (2007) and are listed in Table 14.1. 

In MATLAB, an optional pdetool toolbox allows one to solve 2-D BVPs and to perform various low-level mesh generation and assembly operations. There exists also a more advanced software package, FEMLAB, (www.comsol.com), from the developers of pdetool, that can solve multiple PDEs of various types in two and three dimensions. The supplemental material in the accompanying website contains an example of the use of FEMLAB to model a microftuidic H-filer, requiring the simultaneous solution of the Navier-Stokes equations and a mass balance. A second FEMLAB example in the supplemental material models natural convection between two flat, vertical plates at different temperatures (Figure 6.30). 

Most solutions found by solving the corr5>lete set of piezoelectric material equations are very simple approximations. Computation, typically using finite element analysis software, is often necessary for practical cases. The ability to handle piezoelectric materials in commercially available finite element analysis software varies, though ANSYS (ANSYS Inc., Canonsburg, PA, USA) and COM-SOL (COMSOL Inc., Burlington, MA, USA) are two well-known packages with decent implementations. However, a one-dimensional model of the piezoelectric material behavior offers many of the salient features without the complexity. 

For more complex geometries in two- and three-dimensional space FEM or BEM might be a choice, especially if one has access to commercial FEM software such as ANSYS or COMSOL Multiphysics . In any case, for commercial packages, convergency tests are still necessary to gain insight into the quality of the simulation. 

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