1,142 research outputs found
Exploring the Interplay between CAD and FreeFem++ as an Energy Decision-Making Tool for Architectural Design
The energy modelling software tools commonly used for architectural purposes do not allow
a straightforward real-time implementation within the architectural design programs. In addition,
the surrounding exterior spaces of the building, including the inner courtyards, hardly present
a specific treatment distinguishing these spaces from the general external temperature in the thermal
simulations. This is a clear disadvantage when it comes to streamlining the design process in relation
to the whole-building energy optimization. In this context, the present study aims to demonstrate
the advantages of the FreeFem++ open source program for performing simulations in architectural
environments. These simulations include microclimate tests that describe the interactions between
a building architecture and its local exterior. The great potential of this mathematical tool can be
realized through its complete system integration within CAD (Computer-Aided Design) software
such as SketchUp or AutoCAD. In order to establish the suitability of FreeFem++ for the performance
of simulations, the most widely employed energy simulation tools able to consider a proposed
architectural geometry in a specific environment are compared. On the basis of this analysis,
it can be concluded that FreeFem++ is the only program displaying the best features for the
thermal performance simulation of these specific outdoor spaces, excluding the currently unavailable
easy interaction with architectural drawing programs. The main contribution of this research is,
in fact, the enhancement of FreeFem++ usability by proposing a simple intuitive method for the
creation of building geometries and their respective meshing (pre-processing). FreeFem++ is also
considered a tool for data analysis (post-processing) able to help engineers and architects with
building energy-efficiency-related tasks
A mesh adaptivity scheme on the Landau-de Gennes functional minimization case in 3D, and its driving efficiency
This paper presents a 3D mesh adaptivity strategy on unstructured tetrahedral
meshes by a posteriori error estimates based on metrics, studied on the case of
a nonlinear finite element minimization scheme for the Landau-de Gennes free
energy functional of nematic liquid crystals. Newton's iteration for tensor
fields is employed with steepest descent method possibly stepping in.
Aspects relating the driving of mesh adaptivity within the nonlinear scheme
are considered. The algorithmic performance is found to depend on at least two
factors: when to trigger each single mesh adaptation, and the precision of the
correlated remeshing. Each factor is represented by a parameter, with its
values possibly varying for every new mesh adaptation. We empirically show that
the time of the overall algorithm convergence can vary considerably when
different sequences of parameters are used, thus posing a question about
optimality.
The extensive testings and debugging done within this work on the simulation
of systems of nematic colloids substantially contributed to the upgrade of an
open source finite element-oriented programming language to its 3D meshing
possibilities, as also to an outer 3D remeshing module
A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation
We present a new numerical system using classical finite elements with mesh
adaptivity for computing stationary solutions of the Gross-Pitaevskii equation.
The programs are written as a toolbox for FreeFem++ (www.freefem.org), a free
finite-element software available for all existing operating systems. This
offers the advantage to hide all technical issues related to the implementation
of the finite element method, allowing to easily implement various numerical
algorithms.Two robust and optimised numerical methods were implemented to
minimize the Gross-Pitaevskii energy: a steepest descent method based on
Sobolev gradients and a minimization algorithm based on the state-of-the-art
optimization library Ipopt. For both methods, mesh adaptivity strategies are
implemented to reduce the computational time and increase the local spatial
accuracy when vortices are present. Different run cases are made available for
2D and 3D configurations of Bose-Einstein condensates in rotation. An optional
graphical user interface is also provided, allowing to easily run predefined
cases or with user-defined parameter files. We also provide several
post-processing tools (like the identification of quantized vortices) that
could help in extracting physical features from the simulations. The toolbox is
extremely versatile and can be easily adapted to deal with different physical
models
A pressure impulse theory for hemispherical liquid impact problems
Liquid impact problems for hemispherical fluid domain are considered. By
using the concept of pressure impulse we show that the solution of the flow
induced by the impact is reduced to the derivation of Laplace's equation in
spherical coordinates with Dirichlet and Neumann boundary conditions. The
structure of the flow at the impact moment is deduced from the spherical
harmonics representation of the solution. In particular we show that the slip
velocity has a logarithmic singularity at the contact line. The theoretical
predictions are in very good agreement both qualitatively and quantitatively
with the first time step of a numerical simulation with a Navier-Stokes solver
named Gerris.Comment: 11 pages, 14 figures, Accepted for publication in European Journal of
Mechanics - B/Fluid
An efficient way to assemble finite element matrices in vector languages
Efficient Matlab codes in 2D and 3D have been proposed recently to assemble
finite element matrices. In this paper we present simple, compact and efficient
vectorized algorithms, which are variants of these codes, in arbitrary
dimension, without the use of any lower level language. They can be easily
implemented in many vector languages (e.g. Matlab, Octave, Python, Scilab, R,
Julia, C++ with STL,...). The principle of these techniques is general, we
present it for the assembly of several finite element matrices in arbitrary
dimension, in the P1 finite element case. We also provide an extension of the
algorithms to the case of a system of PDE's. Then we give an extension to
piecewise polynomials of higher order. We compare numerically the performance
of these algorithms in Matlab, Octave and Python, with that in FreeFEM++ and in
a compiled language such as C. Examples show that, unlike what is commonly
believed, the performance is not radically worse than that of C : in the
best/worst cases, selected vector languages are respectively 2.3/3.5 and
2.9/4.1 times slower than C in the scalar and vector cases. We also present
numerical results which illustrate the computational costs of these algorithms
compared to standard algorithms and to other recent ones
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