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Orientador: Carlos Henrique Daros / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-23T13:53:37Z (GMT). No. of bitstreams: 1 Borges_RicardoVendrame_M.pdf: 7836020 bytes, checksum: 6416c1d8724fe2108b090c71bec11800 (MD5) Previous issue date: 2013 / Resumo: A presente dissertação concentra-se no estudo da elasticidade não-linear através do Método dos Elementos de Contorno. A elasticidade não-linear possui um importante campo de aplicações, da simulação de materiais que se comportam como a borracha a novas aplicações como a simulação de tecidos biológicos. A dissertação apresenta como resultado principal a elaboração de um código computacional em Matlab ®, o qual é capaz de modelar materiais elásticos, não-lineares, sujeitos à deformações não-lineares, incrementais. O programa de elementos de contorno foi utilizado na simulação da resposta quasi-estática em materiais incompressíveis como a borracha, aproximados através do modelo constitutivo de Mooney-Rivlin / Abstract: The present work focuses on the modelling of non-linear elastic problems via the Boundary Element Method. Non-linear elasticity has several important applications, from the modelling of rubber-like materials to new areas of research such as the study of biological tissues. The work's main result is the construction of a computer code (in Matlab ®) which can model non-linear elastic materials subjected to incremental non-linear deformations. The code was used within the realm of quasi-static simulations of incompressible rubber-like materials, approximated via the Mooney-Rivlin constitutive model / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestra em Engenharia Mecânica

Orientador: Leandro Palermo Junior / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-24T13:49:30Z (GMT). No. of bitstreams: 1 Millan_LeandroPrearo_D.pdf: 4533018 bytes, checksum: e773a91ae0a43139a214d9f81b444917 (MD5) Previous issue date: 2014 / Resumo: O problema de transferência de calor com controle de temperatura incluindo um algoritmo genético para otimização do processo é estudado neste trabalho. O problema ocorre na terapia de tratamento de câncer denominada hipertermia em que tecidos ao redor do tumor são aquecidos a cerca de 40 ºC por um conjunto de antenas que envolvem o paciente, com orientação em fase e direcionadas a um ponto que recebe calor devido à incidência das ondas eletromagnéticas. O problema de transferência de calor em biosistemas emprega a equação de Pennes e as equações de Maxwell para determinação do campo elétrico e magnético. Um modelo bidimensional é estudado com o Método dos Elementos de Contorno incluindo o Método da Reciprocidade Dual (MECRD). A heterogeneidade do meio pode ser tratada com a associação de vários meios homogêneos pela inclusão de sub-regiões no tratamento pelo MECRD. É proposta uma nova função aproximadora no MECRD para tratar os efeitos de domínio das equações integrais relacionadas às equações de Maxwell e Pennes no regime estacionário, reduzidas a equações não homogêneas do tipo de Helmholtz. A convergência da função é avaliada em exemplos com geometria simples. O modelo foi testado para um caso com tumores em diferentes profundidades sendo os resultados comparados aos disponíveis na literatura / Abstract: The problem of heat transfer with temperature control including a genetic algorithm for optimization of the process is studied in this work. The problem occurs in the cancer therapy called hyperthermia in which tissue around the tumor is heated to about 40 ºC by a set o antennas that involve the patient, with phase orientation and directed to a spot that receives heat due the incidence of electromagnetic waves. The problem o heat transfer in biosystems employs the Pennes¿ equation and Maxwell¿s equations for determining the electric and magnetic field. A two-dimensional model is studied with the Boundary Element Method including the Dual Reciprocity Method (DRBEM). The heterogeneity of the medium can be treated with the combination of various homogeneous media by the inclusion of sub-regions in the DRBEM. It is proposed a new approximating function for DRBEM to treat the domain effects of the integral equations related to Maxwell¿s and Pennes¿ equations in steady state, reduced to non-homogeneous Helmholtz equations. The convergence of the function is evaluated in examples with simple geometry. The model was tested for a case with tumors in different depths been the results compared with the available literature / Doutorado / Estruturas / Doutor em Engenharia Civil

Exascale systems are predicted to have approximately one billion cores, assuming Gigahertz cores. Limitations on affordable network topologies for distributed memory systems of such massive scale bring new challenges to the currently dominant parallel programing model. Currently, there are many efforts to evaluate the hardware and software bottlenecks of exascale designs. It is therefore of interest to model application performance and to understand what changes need to be made to ensure extrapolated scalability. Fast multipole methods (FMM) were originally developed for accelerating N-body problems for particle-based methods in astrophysics and molecular dynamics. FMM is more than an N-body solver, however. Recent efforts to view the FMM as an elliptic PDE solver have opened the possibility to use it as a preconditioner for even a broader range of applications. In this thesis, we (i) discuss the challenges for FMM on current parallel computers and future exascale architectures, with a focus on inter-node communication, and develop a performance model that considers the communication patterns of the FMM for spatially quasi-uniform distributions, (ii) employ this performance model to guide performance and scaling improvement of FMM for all-atom molecular dynamics simulations of uniformly distributed particles, and (iii) demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for satisfying conditions at finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Compared with multilevel methods, FMM is capable of comparable algebraic convergence rates down to the truncation error of the discretized PDE, and it has superior multicore and distributed memory scalability properties on commodity architecture supercomputers. Compared with other methods exploiting the low rank character of off-diagonal blocks of the dense resolvent operator, FMM-preconditioned Krylov iteration may reduce the amount of communication because it is matrix-free and exploits the tree structure of FMM. Fast multipole-based solvers and preconditioners are demonstrably poised to play a leading role in exascale computing.

In this thesis we study hybrid numerical methods to be usedin computational electromagnetics. We restrict the methods tospectral domain and scattering problems. The hybrids consist ofcombinations of Boundary Element Methods and Geometrical Theoryof Diffraction. In the thesis three hybrid methods will be presented. Onemethod has been developped from a theoretical idea to anindustrial code. The two other methods will be presented mainlyfrom a theoretical perspective. We will also give shortintroductions to the Boundary Element Method and theGeometrical Theory of Diffraction from a theoretical andimplementational point of view. <b>Keywords:</b>Maxwell’s equations, Geometrical Theoryof Diffraction, Boundary Element Method, Hybrid methods,Electromagnetic Scattering / NR 20140805

<div>Quantifying the dynamics and rheology of soft biological suspensions such as red blood cells, vesicles, or capsules is paramount to many biomedical and computational applications. These systems are multiphase flows that can contain a diverse set of deformable cells and rigid bodies with complex wall geometries. For this thesis, we are performing several numerical simulations using boundary element methods (BEM) for biological suspensions in biomedically relevant conditions. Each simulation is devised to answer fundamental questions in modeling these systems.</div><div><br></div><div><br></div><div>Part of this thesis centers around the fluid mechanics of giant unilamellar vesicles (GUVs), fluid droplets surrounded by a phospholipid bilayer. GUVs are important to study because they mimic the dynamics of anuclear cells and are commonly used as a basis for artificial cells. The dynamics of vesicles in simple shear or extensional flows have been extensively studied. However the conditions seen in microfluidic devices or industrial processing are not always described by steady shear or extensional flows alone, and require more investigation. In our first study, we investigate the shape stability of osmotically deflated vesicles in a general linear flow (i.e., linear combinations of extensional and rotational flows). We modeled the vesicles as a droplet with an incompressible interface with a bending resistance. We simulated a range of flow types from purely shear to purely extensional at viscosity ratios ranging from 0.01 to 5.0 and reduced volumes (measured asphericity, higher is more spherical) from 0.60 to 0.70. The vesicle's viscosity ratio appears to play a minimal role in describing its shape and stability for many mixed flows, even in cases when significant flows are present in the vesicle interior. We find in these cases that the bending critical capillary number for shape instabilities collapse onto similar values if the capillary number is scaled by an effective extensional rate. These results contrast with droplet studies where both viscosity ratio and flow type have significant effects on breakup. Our simulations suggest that if the flow type is not close to pure shear flow, one can accurately quantify the shape and stability of vesicles using the results from an equiviscous vesicle in pure extension. Only when the flow type is nearly shear flow, do we start to see deviations in the observations discussed above. In this situation, the vesicle's stationary shape develops a shape deviation, which introduces a stabilizing effect and makes the critical capillary number depend on the viscosity ratio.</div><div><br></div><div><br></div><div>Continuing with our research on single vesicle dynamics, we have performed simulations and experiments on vesicles in large amplitude oscillatory extensional (LAOE) flows. By using LAOE we can probe the non-linear extension and compression of vesicles and how these types of deformation affect dilute suspension microstructure in time-dependent flows through contractions, expansions, or other complex geometries. Our numerical and experimental results for vesicles of reduced volumes from 0.80 to 0.95 have shown there to be three general dynamical regimes differentiated by the amount of deformation that occurs in each half cycle. We have termed the regimes: symmetrical, reorienting, and pulsating in reference to the type of deformation that occurs. We find the deformation of the quasispherical vesicles in the microfluidic experiments and boundary element simulations to be in quantitative agreement. The distinct dynamics observed in each regime result from a competition between the flow frequency, flow time scale, and membrane deformation timescale. Using the numerical results, we calculate the particle coefficient of stresslet and quantify the nonlinear relationship between average vesicle stress and strain rate. We additionally present some results on the dynamics of tubular vesicles in LAOE, showing how the experiments suggest the vesicles undergo a shape transformation over several strain rate cycles. Broadly, our work provides new information regarding the transient dynamics of vesicles in time-dependent flows that directly informs bulk suspension rheology.</div><div><br></div><div><br></div><div>Our most recent project deals with the accuracy of discretized double layer integrals for Stokes flow in the boundary element method.</div><div>In the fluid mechanics literature, the chosen parameterization, meshing procedure, and singularity handling are often selected arbitrarily or based on a convergence study where the number of elements is decreased until the relative error is sufficiently low.</div><div>A practical study on the importance of each of these parameters to the accurate calculation of physically relevant results, such as the particle stresslet, could alleviate some of the guesswork required. The analytical formulas for the eigenfunctions/eigenvalues of the double layer operator of an ellipsoidal particle in a quadratic flow were recently published¹, providing an analytical basis for testing boundary element method discretization accuracy.</div><div>We use these solutions to examine the local and global errors produced by changing the interpolation order of the geometry and the double-layer density. The results show that the local errors can be significant even when the global errors are small, prompting additional study on the distribution of local errors. Interestingly, we find that increasing the interpolation orders for the geometry and the double layer density does not always guarantee smaller errors. Depending on the nature of the meshing near high curvature regions, the number of high aspect ratio elements, and the flatness of the particle geometry, a piecewise-constant density can exhibit lower errors than piecewise-linear density, and there can be little benefit from using curved triangular elements. Overall, this study provides practical insights on how to appropriately discretize and parameterize three-dimensional (3D) boundary-element simulations for elongated particles with prolate-like and oblate-like geometries.</div><div><br></div>

In contrast to the structural modes, which describe the physical motion of vibrating structures, acoustic radiation modes describe the radiated sound power. Radiation modes are beneficial in active noise control because reducing an efficiently radiating radiation mode guarantees the reduction of radiated sound power. Much work has been done to calculate the radiation modes for simple geometries, where analytic solutions are available. In this work, isogeometric analysis (IGA) is used to provide a tool capable of analyzing the radiation modes of arbitrarily complex geometries. IGA offers increased accuracy and efficiency by using basis functions generated from Non-Uniform Rational B-Splines (NURBS) or T-Splines, which can represent geometries exactly. Results showing this increased accuracy and efficiency with IGA using T-Splines are shown for a sphere to validate the method, comparing with the exact analytical solution as well as results from a traditional boundary element method. A free cylindrical shell is also analyzed to show the usefulness of this method. Expected similarities, as well as expected differences, are observed between this free shell and a baffled cylindrical shell.

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