GRAPH GRAMMAR BASED PETRI NET CONTROLLED DIRECT SOLVER ALGORITHM

In this paper we present the Petri net setting the optimal order of elimination for directsolver working with hp refined finite finite element meshes. The computational mesh is representedby a graph, with graph vertices corresponding to finite element nodes. The directsolver algorithm is expressed as a sequence of graph grammar productions, attributing thegraph vertices. The Petri net dictates the order of graph grammar productions, representingthe execution of the solver algorithm over a graph representation of computational mesh.The presentation is concluded with numerical experiments performed for a model L-shapedomain

Anisotropic 2D mesh adaptation in hp-adaptive FEM

AbstractThe paper presents a grammar for anisotropic two-dimensional mesh adaptation in hp-adaptive Finite Element Method with rectangular elements. It occurs that a straightforward approach to modeling this process via grammar productions leads to potential deadlock in h-adaptation of the mesh. This fact is shown on a Petri net model of an exemplary adaptation. Therefore auxiliary productions are added to the grammar in order to ensure that any sequence of productions allowed by the grammar does not lead to a deadlock state. The fact that the enhanced grammar is deadlock-free is proven via a corresponding Petri net model. The proof has been performed by means of reachability graph construction and analysis. The paper is enhanced with numerical simulations of magnetolluric measurements where the deadlock problem occured

A summary of my twenty years of research according to Google Scholars

I am David Pardo, a researcher from Spain working mainly on numerical analysis applied to geophysics. I am 40 years old, and over a decade ago, I realized that my performance as a researcher was mainly evaluated based on a number called \h-index". This single number contains simultaneously information about the number of publications and received citations. However, dif- ferent h-indices associated to my name appeared in di erent webpages. A quick search allowed me to nd the most convenient (largest) h-index in my case. It corresponded to Google Scholars. In this work, I naively analyze a few curious facts I found about my Google Scholars and, at the same time, this manuscript serves as an experiment to see if it may serve to increase my Google Scholars h-index

A summary of my twenty years of research according to Google Scholars

I am David Pardo, a researcher from Spain working mainly on numerical analysis applied to geophysics. I am 40 years old, and over a decade ago, I realized that my performance as a researcher was mainly evaluated based on a number called \h-index". This single number contains simultaneously information about the number of publications and received citations. However, dif- ferent h-indices associated to my name appeared in di erent webpages. A quick search allowed me to nd the most convenient (largest) h-index in my case. It corresponded to Google Scholars. In this work, I naively analyze a few curious facts I found about my Google Scholars and, at the same time, this manuscript serves as an experiment to see if it may serve to increase my Google Scholars h-index

Graph grammar-based multi-frontal parallel direct solver for two-dimensional isogeometric analysis

This paper introduces the graph grammar based model for developing multi-thread multi-frontal parallel direct solver for two dimensional isogeometric finite element method. Execution of the solver algorithm has been expressed as the sequence of graph grammar productions. At the beginning productions construct the elimination tree with leaves corresponding to finite elements. Following sequence of graph grammar productions generates element frontal matrices at leaf nodes, merges matrices at parent nodes and eliminates rows corresponding to fully assembled degrees of freedom. Finally, there are graph grammar productions responsible for root problem solution and recursive backward substitutions. Expressing the solver algorithm by graph grammar productions allows us to explore the concurrency of the algorithm. The graph grammar productions are grouped into sets of independent tasks that can be executed concurrently. The resulting concurrent multi-frontal solver algorithm is implemented and tested on NVIDIA GPU, providing O(NlogN) execution time complexity where N is the number of degrees of freedom. We have confirmed this complexity by solving up to 1 million of degrees of freedom with 448 cores GPU. © 2012 Published by Elsevier Ltd

Applied novel software development methodology for process engineering application

Chemical processes are nonlinear continuous/discrete dynamic systems that are subject to considerable uncertainties and variations during their design and operation. These systems are designed to operate at an economically optimal steady-state. However, minor changes in process parameters’ values might cause deviations and elicit dynamic responses from processes. Controllability—defined as the ability of holding a process within a specified operating regime and the controllability assessment of each given process system—should be taken into account during the system design phase. This emphasises the necessity of effective software tools that could assist process engineers in their controllability evaluation. Although there are few multipurpose tools available for this task, developing software tools for controllability analysis is a tedious and sophisticated undertaking. It involves elaboration from multiple disciplines, and the requirements of controllability assessments are so vast that it is almost impossible to create general software that covers all controllability measures and cases. This thesis aims to systematically tackle the challenge of developing practical and high-quality software tools for controllability problems while reducing the required time and effort, regardless of the size and scale of the controllability problem. Domain-specific language (DSL) methodology is proposed for this purpose. DSLs are programming languages designed to address the programming problems of a specific domain. Therefore, well-designed DSLs are simple, easy to use and capable of solving any problem defined in their domains. Based on DSL methodology, this study proposes a four-element framework to partition the software system into decoupled elements, and discusses the design and implementation steps of each element as well as communication between elements. The superiority of the developed methodology based on DSL is compared with traditional programming techniques for controllability assessment of various case studies. Essentially, the major advantage of the proposed methodology is the performance of the software product. Performance measures used in this study are total time to develop (TD) the software tool and its modifiability. Total time and effort to implement and use the result products presents up to five times improvement. Moreover, the result product’s modifiability is assessed by applying modifications, which also demonstrates up to five times improvement. All measures are tested on continuous stirred-tank reaction (CSTR) and forced-circulation evaporator (FCE) case studies. In conclusion, this study significantly contributes to two fields. The first is DSL, since this thesis studies different types of DSLs and evaluates their applications in the controllability analysis. The second is the controllability evaluation, since this study examines a new methodology for software development in controllability assessment

Tools and Algorithms for the Construction and Analysis of Systems

This open access two-volume set constitutes the proceedings of the 27th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2021, which was held during March 27 – April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The total of 41 full papers presented in the proceedings was carefully reviewed and selected from 141 submissions. The volume also contains 7 tool papers; 6 Tool Demo papers, 9 SV-Comp Competition Papers. The papers are organized in topical sections as follows: Part I: Game Theory; SMT Verification; Probabilities; Timed Systems; Neural Networks; Analysis of Network Communication. Part II: Verification Techniques (not SMT); Case Studies; Proof Generation/Validation; Tool Papers; Tool Demo Papers; SV-Comp Tool Competition Papers