Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Computer Aided Verification

The open access two-volume set LNCS 12224 and 12225 constitutes the refereed proceedings of the 32st International Conference on Computer Aided Verification, CAV 2020, held in Los Angeles, CA, USA, in July 2020.* The 43 full papers presented together with 18 tool papers and 4 case studies, were carefully reviewed and selected from 240 submissions. The papers were organized in the following topical sections: Part I: AI verification; blockchain and Security; Concurrency; hardware verification and decision procedures; and hybrid and dynamic systems. Part II: model checking; software verification; stochastic systems; and synthesis. *The conference was held virtually due to the COVID-19 pandemic

Reliability-based design and topology optimization of aerospace components and structures

Programa de doutoramento en Enxeñaría Civil. 5011V01[Abstract] This work presents a research on Reliability Analysis (RA) and Reliability-Based Design Optimization (RBDO) with the target of solving practical aerospace structures problems. Two types of problems are considered, each one solved with a different approach. The first one applies Reliability-Based Topology Optimization (RBTO) to industry-like aerospace structures, while the second performs RBDO on aerospace components that require meticulous and computationally expensive simulations in order to predict accurately their behaviour. The RBDO method used in both approaches is the Sequential Optimization and Reliability Assessment (SORA) due to its uncoupled nature, which allows to separate the Deterministic Optimization (DO) and RA phases being easily combinable with external software. On the other hand, the RA method selected is the Hybrid Mean Value (HMV) given its robustness. Both algorithms have been implemented in MATLAB codes working in a High Performance Computing (HPC) environment. In the first approach they are combined with an external optimization software (Altar Optistruct) able to perform Deterministic Topology Optimization (DTO) problems. In the second approach the MATLAB codes are combined with external Finite Element (FE) analysis software (Abaqus), and the RA phase benefits from a Polynomial Chaos Expansion (PCE) based metamodel in order to save computating time. Several application examples have been carried out, including a wing, a rear fuselage and a pylon in the first approach and a stiffened composite panel in the second approach.[Resumen] Este trabajo presenta una investigación en análisis de fiabilidad (RA) y diseño óptimo en entornos de incertidumbre (RBDO) con el objetivo de resolver problemas prácticos de estructuras aeroespaciales. Se han considerado dos tipos de problema, cada uno siendo resuelto con un enfoque diferente. En el primero se aplica optimización topológica en entornos de incertidumbre (RBTO) a estructuras aeroespaciales similares a las que se pueden encontrar en un contexto industrial, mientras que el segundo aplica RBDO a componentes aeroespaciales que requieren simulaciones minuciosas y costosas computacionalmente para predecir correctamente su comportamiento. El método de RBDO usado en ambos enfoques es el de optimización y evaluación de fiabilidad secuencial (SORA) debido a su naturaleza desacoplada, que permite separar las fases de optimización determinista (DO) y RA siendo fácilmente combinable con software externos. Por otro lado, el método de RA seleccionado es el valor medio híbrido (HMV) debido a su robustez. Ambos algoritmos se han implementado en códigos de MATLAB que trabajan en ambientes de computación de alto rendimiento (HPC). En el primer enfoque se combinan con un software de optimización externo (Altair Optistruct) capaz de resolver problemas de optimización topológica determinista (DTO). En el segundo enfoque los códigos de MATLAB se combinan con un software de análisis de elementos finitos (FE) externo (Abaqus), y la fase de RA se beneficia de un metamodelo basado en la expansión polinómica del caos (PCE) para ahorrar coste computacional. En este marco de referencia, se han resuelto varios ejemplos, que incluyen un ala, la parte trasera de un fuselaje y un pilono para el primer enfoque y un panel rigidizado de material compuesto en el segundo enfoque.[Resumo] Este traballo presenta unha investigación en análise de fiabilidade (RA) e deseño óptimo en contornas de incerteza (RBDO) co obxectivo de resolver problemas prácticos de estruturas aeroespaciais. Consideráronse dous tipos de problema, cada un sendo resolto cun enfoque diferente. No primeiro aplícase optimización topolóxica en contornas de incerteza (RBTO) a estruturas aeroespaciais similares ás que se poden atopar nun contexto industrial, mentres que o segundo aplica RBDO a compoñentes aeroespaciais que requiren simulacións minuciosas e custosas computacionalmente para predicir correctamente o seu comportamento. O método de RBDO usado en ambos os enfoques é o de optimización e avaliación de fiabilidade secuencial (SORA) debido á súa natureza desacoplada, que permite separar as fases de optimización determinista (DO) e RA sendo facilmente combinable con software externos. Doutra banda, o método de RA seleccionado é o valor medio híbrido (HMV) debido á súa robustez. Ambos os algoritmos implementáronse en códigos de MATLAB que traballan en ambientes de computación de alto rendemento (HPC). No primeiro enfoque combínanse cun software de optimización externo (Altair Optistruct) capaz de resolver problemas de optimización topolóxica determinista (DTO). No segundo enfoque os códigos de MATLAB combínanse cun software de análise de elementos finitos (FE) externo (Abaqus), e a fase de RA benefíciase dun metamodelo baseado na expansión polinómica do caos (PCE) para aforrar custo computacional. Neste marco de referencia, resolvéronse varios exemplos, que inclúen un á, a parte traseira dunha fuselaxe e un pilono para o primeiro enfoque e un panel rixidizado de material composto no segundo enfoque