85 research outputs found
Parallel computations based on domain decompositions and integrated radial basis functions for fluid flow problems
The thesis reports a contribution to the development of parallel algorithms based on Domain Decomposition (DD) method and Compact Local Integrated Radial Basis Function (CLIRBF) method. This development aims to solve large scale
fluid flow problems more efficiently by using parallel high performance computing (HPC). With the help of the DD method, one big problem can be separated into sub-problems and solved on parallel machines. In terms of numerical analysis, for each sub-problem, the overall condition number of the system matrix is significantly reduced. This is one of the main reasons for the stability, high
accuracy and efficiency of parallel algorithms. The developed methods have been successfully applied to solve several benchmark problems with both rectangular
and non-rectangular boundaries.
In parallel computation, there is a challenge called Distributed Termination Detection (DTD) problem. DTD concerns the discovery whether all processes in a
distributed system have finished their job. In a distributed system, this problem is not a trivial problem because there is neither a global synchronised clock nor
a shared memory. Taking into account the specific requirement of parallel algorithms, a new algorithm is proposed and called the Bitmap DTD. This algorithm
is designed to work with DD method for solving Partial Differential Equations (PDEs). The Bitmap DTD algorithm is inspired by the Credit/Recovery DTD class (or weight-throw). The distinguishing feature of this algorithm is the use of a bitmap to carry the snapshot of the system from process to process. The proposed algorithm possesses characteristics as follows. (i) It allows any process to
detect termination (symmetry); (ii) it does not require any central control agent (decentralisation); (iii) termination detection delay is of the order of the diameter of the network; and (iv) the message complexity of the proposed algorithm is optimal.
In the first attempt, the combination of the DD method and CLIRBF based collocation approach yields an effective parallel algorithm to solve PDEs. This approach has enabled not only the problem to be solved separately in each subdomain by a Central Processing Unit (CPU) but also compact local stencils to be independently treated. The present algorithm has achieved high throughput
in solving large scale problems. The procedure is illustrated by several numerical examples including the benchmark lid-driven cavity flow problem.
A new parallel algorithm is developed using the Control Volume Method (CVM) for the solution of PDEs. The goal is to develop an efficient parallel algorithm
especially for problems with non-rectangular domains. When combined with CLIRBF approach, the resultant method can produce high-order accuracy and economical solution for problems with complex boundary. The algorithm is verified
by solving two benchmark problems including the square lid-driven cavity flow and the triangular lid-driven cavity flow. In both cases, the accuracy is in great agreement with benchmark values. In terms of efficiency, the results show that the method has a very high efficiency profile and for some specific cases a super-linear speed-up is achieved.
Although overlapping method yields a straightforward implementation and stable convergence, overlapping of sub-domains makes it less applicable for complex
domains. The method even generates more computing overhead for each subdomain as the overlapping area grows. Hence, a parallel algorithm based on non-overlapping DD and CLIRBF has been developed for solving Navier-Stokes
equations where a CLIRBF scheme is used to solve the problem in each subdomain. A relaxation factor is employed for the transmission conditions at the interface of sub-domains to ensure the convergence of the iterative method while the Bitmap DTD algorithm is used to achieve the global termination. The parallel algorithm is demonstrated through two fluid flow problems, namely the natural
convection in concentric annuli (Boussinesq fluids) and the lid-driven cavity flow (viscous fluids). The results confirm the high efficiency of the present method in
comparison with a sequential algorithm. A super-linear efficiency is also observed for a range of numbers of CPUs.
Finally, when comparing the overlapping and non-overlapping parallel algorithms, it is found that the non-overlapping one is less stable. The numerical results show that the non-overlapping method is not able to converge for high Reynolds number while overlapping method reaches the same convergence profile as the sequential CLIRBF method. Thus, in this research when dealing with non-Newtonian
fluids and large scale problems, the overlapping method is preferred to the nonoverlapping one. The flow of Oldroyd-B fluid through a planar contraction was considered as a benchmark problem. In this problem, the singularity of stress at the re-entrant corners always poses difficulty to numerical methods in obtaining stable solutions at high Weissenberg numbers. In this work, a high resolution
simulation of the flow is obtained and the contour of streamline is shown to be in great agreement with other results
A three-dimensional finite element approach for predicting the transmission loss in mufflers and silencers with no mean flow
A three-dimensional finite element method has been implemented to predict the transmission loss of a packed muffler and a parallel baffle silencer for a given frequency range. Iso-parametric quadratic tetrahedral elements have been chosen due to their flexibility and accuracy in modeling geometries with curved surfaces. For accurate physical representation, perforated plates are modeled with complex acoustic impedance while absorption linings are modeled as a bulk media with a complex speed of sound and mean density. Domain decomposition and parallel processing techniques are applied to address the high computational and memory requirements. The comparison of the computationally predicted and the experimentally measured transmission loss shows a good agreement
Rotary Wing Aerodynamics
This book contains state-of-the-art experimental and numerical studies showing the most recent advancements in the field of rotary wing aerodynamics and aeroelasticity, with particular application to the rotorcraft and wind energy research fields
Cartesian grid FEM (cgFEM): High performance h-adaptive FE analysis with efficient error control. Application to structural shape optimization
More and more challenging designs are required everyday in today¿s industries.
The traditional trial and error procedure commonly used for mechanical
parts design is not valid any more since it slows down the design process and
yields suboptimal designs. For structural components, one alternative consists
in using shape optimization processes which provide optimal solutions.
However, these techniques require a high computational effort and require
extremely efficient and robust Finite Element (FE) programs. FE software
companies are aware that their current commercial products must improve in
this sense and devote considerable resources to improve their codes. In this
work we propose to use the Cartesian Grid Finite Element Method, cgFEM
as a tool for efficient and robust numerical analysis. The cgFEM methodology
developed in this thesis uses the synergy of a variety of techniques to achieve
this purpose, but the two main ingredients are the use of Cartesian FE grids
independent of the geometry of the component to be analyzed and an efficient
hierarchical data structure. These two features provide to the cgFEM
technology the necessary requirements to increase the efficiency of the cgFEM
code with respect to commercial FE codes. As indicated in [1, 2], in order to
guarantee the convergence of a structural shape optimization process we need
to control the error of each geometry analyzed. In this sense the cgFEM code
also incorporates the appropriate error estimators. These error estimators are
specifically adapted to the cgFEM framework to further increase its efficiency.
This work introduces a solution recovery technique, denoted as SPR-CD, that in combination with the Zienkiewicz and Zhu error estimator [3] provides very
accurate error measures of the FE solution. Additionally, we have also developed
error estimators and numerical bounds in Quantities of Interest based
on the SPR-CD technique to allow for an efficient control of the quality of
the numerical solution. Regarding error estimation, we also present three new
upper error bounding techniques for the error in energy norm of the FE solution,
based on recovery processes. Furthermore, this work also presents an
error estimation procedure to control the quality of the recovered solution in
stresses provided by the SPR-CD technique. Since the recovered stress field
is commonly more accurate and has a higher convergence rate than the FE
solution, we propose to substitute the raw FE solution by the recovered solution
to decrease the computational cost of the numerical analysis. All these
improvements are reflected by the numerical examples of structural shape optimization
problems presented in this thesis. These numerical analysis clearly
show the improved behavior of the cgFEM technology over the classical FE
implementations commonly used in industry.Cada d'¿a dise¿nos m'as complejos son requeridos por las industrias actuales.
Para el dise¿no de nuevos componentes, los procesos tradicionales de prueba y
error usados com'unmente ya no son v'alidos ya que ralentizan el proceso y dan
lugar a dise¿nos sub-'optimos. Para componentes estructurales, una alternativa
consiste en usar procesos de optimizaci'on de forma estructural los cuales
dan como resultado dise¿nos 'optimos. Sin embargo, estas t'ecnicas requieren
un alto coste computacional y tambi'en programas de Elementos Finitos (EF)
extremadamente eficientes y robustos. Las compa¿n'¿as de programas de EF
son conocedoras de que sus programas comerciales necesitan ser mejorados
en este sentido y destinan importantes cantidades de recursos para mejorar
sus c'odigos. En este trabajo proponemos usar el M'etodo de Elementos Finitos
basado en mallados Cartesianos (cgFEM) como una herramienta eficiente
y robusta para el an'alisis num'erico. La metodolog'¿a cgFEM desarrollada en
esta tesis usa la sinergia entre varias t'ecnicas para lograr este prop'osito, cuyos
dos ingredientes principales son el uso de los mallados Cartesianos de EF independientes
de la geometr'¿a del componente que va a ser analizado y una
eficiente estructura jer'arquica de datos. Estas dos caracter'¿sticas confieren
a la tecnolog'¿a cgFEM de los requisitos necesarios para aumentar la eficiencia
del c'odigo cgFEM con respecto a c'odigos comerciales. Como se indica en
[1, 2], para garantizar la convergencia del proceso de optimizaci'on de forma
estructural se necesita controlar el error en cada geometr'¿a analizada. En
este sentido el c'odigo cgFEM tambi'en incorpora los apropiados estimadores de error. Estos estimadores de error han sido espec'¿ficamente adaptados al
entorno cgFEM para aumentar su eficiencia. En esta tesis se introduce un
proceso de recuperaci'on de la soluci'on, llamado SPR-CD, que en combinaci'on
con el estimador de error de Zienkiewicz y Zhu [3], da como resultado medidas
muy precisas del error de la soluci'on de EF. Adicionalmente, tambi'en se han
desarrollado estimadores de error y cotas num'ericas en Magnitudes de Inter'es
basadas en la t'ecnica SPR-CD para permitir un eficiente control de la calidad
de la soluci'on num'erica. Respecto a la estimaci'on de error, tambi'en se presenta
un proceso de estimaci'on de error para controlar la calidad del campo
de tensiones recuperado obtenido mediante la t'ecnica SPR-CD. Ya que el
campo recuperado es por lo general m'as preciso y tiene un mayor orden de
convergencia que la soluci'on de EF, se propone sustituir la soluci'on de EF por
la soluci'on recuperada para disminuir as'¿ el coste computacional del an'alisis
num'erico. Todas estas mejoras se han reflejado en esta tesis mediante ejemplos
num'ericos de problemas de optimizaci'on de forma estructural. Los resultados
num'ericos muestran claramente un mejor comportamiento de la tecnolog'¿a
cgFEM con respecto a implementaciones cl'asicas de EF com'unmente usadas
en la industria.Nadal Soriano, E. (2014). Cartesian grid FEM (cgFEM): High performance h-adaptive FE analysis with efficient error control. Application to structural shape optimization [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/35620TESI
Forecasting with Dynamic Factor Models in both finite and infinite dimensional factor spaces.
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