33º Congresso Nacional de Matemática Aplicada e Computacional
Programação de Conferências
| Conferencistas | Área |
|---|---|
| Michele Benzi Department of Mathematics and Computer Science at Emory University (USA) |
Álgebra Linear Computacional |
| Ralf Deiterding Oak Ridge Laboratory (USA) |
Esquemas numericos adaptativos para PDE (AMR), paralelismo |
| Otto D. L. Strack University of Minnesota (USA) |
Analytic Element Method (AEM) |
| Marcus Aloizio Martinez de Aguiar Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin, Departamento de Física do Estado Sólido e Ciência dos Materiais. |
Sistemas complexos-dinâmica de populações |
| Iain Duff Rutherford Appleton Laboratory/CERFACS (Inglaterra/França) Harwell Science and Innovation Campus |
Numerical Analysis/Sparse Matrices |
| Marcos Nereu Arenales ICMC/USP - São Carlos |
Otimização combinatória |
| Dimitar Kolev Dimitrov IBILCE/UNESP |
Teoria da Aproximação |
Resumos
Título: Parallel Adaptive Cartesian Upwind Methods for Shock-driven Multiphysics Simulation
Ralf Deiterding
Computer Science and Mathematics Division, Oak Ridge National Laboratory
Área: Esquemas numericos adaptativos para PDE (AMR), paralelismo
Finite-volume-based shock-capturing methods can most easily be constructed on structured Cartesian meshes. Implementations of higher order discretizations on unstructured grids, on the other hand, can be quite cumbersome. In this talk, an approach in utilizing Cartesian schemes for real-world problems will be presented that combines the ghost-fluid idea with block-structured adaptive mesh refinement. A scalar level set function storing the distance information to the boundary surface is used to consider arbitrary geometries on the Cartesian mesh without ambiguities. Although the boundary incorporation is of first-order accuracy, several examples from compressible gas dynamics will be presented which demonstrate that the utilization of mesh adaptation makes the overall approach suitable for serious computational investigations.
The method has been implemented in the generic fluid solver framework AMROC that is part of the Virtual Test Facility (VTF) software (_http://www.cacr.caltech.edu/asc_). A temporal splitting approach will be described that couples the adaptive Eulerian finite volume method to explicit Lagrangian finite element schemes for computational solid dynamics. Three-dimensional fluid-structure interaction simulations involving large plastic deformations and/or fracture and fragmentation will be shown that confirm the applicability of the proposed techniques to problems with heavily evolving topology. Results obtained with different solid mechanics solvers coupled to AMROC will be compared, and the parallel performance of the fluid solver and the coupled software will be addressed. Essential auxiliary algorithms and software engineering aspects will be discussed. Where they are non-standard, e.g., for gas-liquid flows or detonation waves with detailed chemical kinetics, the employed finite volume schemes and numerical flux functions will be described briefly.
Título: The generating analytic element approach with application to the modified Helmholtz equation
O. D. L. Strack
University of Minnesota (USA)
Abstract In this paper a new method for obtaining functions with a given singular behavior that satisfy a class of partial differential equations is presented. Differential equations of this class contain operators of the form !2n, where n is a positive integer. The method uses Wirtinger calculus which enables one to invert the Laplacian in combination with the decomposition method introduced by Adomian at the end of the twentieth century. The procedure uses a singular holomorphic function as its basis, and constructs the solution term by term as an infinite series of functions; the process consists of an infinite number of steps of integration. This method is applied to construct a number of singular solutions to the modified Helmholtz equation in the context of groundwater flow. These functions are discharge potentials, which are two-dimensional functions by definition. The gradient of the discharge potential is the vertically integrated flow over the thickness of an aquifer, or water-bearing layer. The discharge potentials of interest here are those used in the analytic element method. This method, as originally conceived, relies on the superposition of suitably chosen holomorphic functions, and is a form of a method known as the Trefftz method, not to be confused with the Trefftz method applied to finite element techniques. The main analytic elements used are singular line elements, characterized by either a jump along the element In the tangential or the normal component of the discharge vector. The analytic line elements for the case of divergence-free irrotational flow are well established and many of these are forms of singular Cauchy integrals. Application of the analytic element method to more general cases of flow, governed for example by the modified Helmholtz equation (flow in systems of aquifers separated by leaky layers) and the heat equation (transient flow) is possible using the method presented in this paper. The latter application is beyond the scope of this paper, but it is worth noting that for that case the constant that occurs in the modified Helmholtz is replaced by a general function of time and application of Laplace transforms can be avoided. A method for constructing such functions is presented; the procedure for constructing these functions is referred to as the generating analytic element approach. Application of this approach requires the existence of the holomorphic singular line element. The approach is discussed and an example for the case of a line-sink for a system of two aquifers separated by a leaky layer and bounded above by in impermeable boundary is presented.
Keywords Analytic element method · Groundwater flow · Modified Helmholtz equation · Superposition of solutions · Wirtinger calculus
Título: A Neutral Theory of Speciation and Diversity
Marcus Aloizio Martinez de Aguiar
Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin, Departamento de Física do Estado Sólido e Ciência dos Materiais.
Área: Sistemas complexos-dinâmica de populações
Resumo: The number of living species on Earth has been estimated to be between 10 and 100 million. Understanding the processes that have generated such remarkable diversity is one of the greatest challenges in evolutionary biology. Speciation is usually related to the isolation of subpopulations by geographic barriers, that stop the genetic flow between the isolated groups, promoting differentiations by mutations and local adaptations that ultimately lead to speciation. In this talk I will dicuss a new mechanism of speciation that does not involve geographical barriers and natural selection. I will present simulations where a population with genetically identical individuals, homogeneously distributed in space, spontaneously breaks up into species when subjected to mutations and to two mating restrictions: individuals can select a mate only from within a maximum spatial distance S from itself and only if the genetic distance between itself and the selected partner is less than a maximum value G. Species develop depending on the mutation rate and on the parameters S and G. The resulting species-area relationships and abundance distributions thus obtained are consistent with observations in nature.
Título: Uma abordagem por otimização linear no plantio sustentável de vegetais
Marcos Nereu Arenales
ICMC/USP - São Carlos
Área: Otimização combinatória
Título: Zeros de Polinômios e de Funções Inteiras
Dimitar Kolev Dimitrov
IBILCE/UNESP
Área: Teoria da Aproximação
Resumo: O Teorema Fundamental da Álgebra afirma que todo polinômio de grau n possui exatamente n zeros complexos.
O problema de encontrar esses zeros explicitamente vem desafiando os matemáticos desde a época medieval. Surpreendentemente, a maioria das conjecturas e hipóteses importantes na matemática pode ser formulada como problemas sobre caracterização de zeros de certos polinômios e também de classes de polinômios ou de funções que possuem zeros em determinadas regiões do plano complexo.
Um exemplo típico vem da Teoria da Estabilidade, onde o comportamento de soluções de equações diferencias depende da localização dos zeros dos polinômios característicos associados às equações. Discutiremos alguns problemas interessantes sobre zeros de polinômios, suas relações com conjecturas e hipóteses que desafiam matemáticos, e suas aplicações.
