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Performance of the multigrid method with time-stepping to solve 1D and 2D wave equations

International Journal for Computational methods in engineering Science and Mechanics 2022年第1期23卷 45-56页

作者： Malacarne, Maicon F. Pinto, Marcio A. V. Franco, Sebastião R. Graduate Program on Numerical Methods in Engineering–PPGMNE Federal University of Parana–UFPR PR Curitiba Brazil Department of Mechanical Engineering Federal University of Parana–UFPR PR Curitiba Brazil Department of Mathematics State University of Centro-Oeste–UNICENTRO PR Irati Brazil

This work aims to discuss a proposed solution for wave equations that utilize discretization by means of the finite difference method, weighted by a parameter η, with sweeping done according to the time-stepping method. The multigrid method is employed to speed up the convergence in obtaining the solution of the system of equations resulting from the discretization. To validate the proposed model, the discretization errors, effective and apparent orders, convergence factor, orders of complexity, and the computational time were assessed. A comparison between the singlegrid and multigrid methods was carried out in order to determine the most advantageous one. © 2021 Taylor & Francis Group, LLC.

关键词： Wave equations

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A Python-Based Study of Resonant Processes in Electric Circuits 37

A Python-Based Study of Resonant Processes in Electric Circu...

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37th International Conference on Information Technologies, InfoTech 2023

作者： Hinov, Nikolay Popov, Stoyan Technical University of Sofia Faculty of Electronic Engineering and Technologies Department of Power Electronics Sofia1000 Bulgaria Technical University of Sofia Faculty of Applied Mathematics and Informatics Department of Mathematical Modeling and Numerical Methods Sofia1000 Bulgaria

ISBN: (纸本)9798350338058

The manuscript presents a study of resonance processes in electrical circuits with the Python programming language. Basic resonant circuits with series and parallel resonance are considered. The obtained results were compared and verified with computer simulations implemented with the popular LTspice program simulator. In this way, the possibilities of researching different electrical circuits with Python have been proven. This is convenient in view of Python's better data collection, processing and analysis capabilities compared to standard Spice-based simulators. In addition, the presented approach is useful for implementation in the learning process of software engineers, where it is important to use different software tools in the study of fundamental disciplines such as electrical engineering and electronics. © 2023 IEEE.

关键词： Python

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Efficient simulation of waves in heterogeneous domains using the scaled boundary finite element method

Efficient simulation of waves in heterogeneous domains using...

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92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics, GAMM 2022

作者： Nattoji-Shara, Sharath Birk, Carolin Gravenkamp, Hauke University of Duisburg-Essen Universitätsstraße 2 Essen45141 Germany International Centre for Numerical Methods in Engineering UPC Campus Nord Edifici C1 Barcelona08034 Spain

Simulation of wave propagation phenomena is very challenging due to the restrictions placed on the spatial as well as on the temporal discretization. Image-based domain discretization using hierarchical meshes (2D polygonal elements) in conjunction with the scaled boundary finite element method provides an efficient numerical simulation tool. In this setting, the computational effort is reduced as only a limited number of unique cell patterns are formed. This is beneficial while computing element matrices in the preprocessing stage. When solving the dynamic system, the advantages of similar elements can only be fully exploited for the explicit time-stepping schemes in connection with mass lumping when the domain is discretized using low-order elements (p ≤ 2). On the other hand, the time step size may be limited by the stability criterion. Moreover, high-order elements require fewer degrees of freedom. Hence for a specific application, it is not straightforward to predict superiority of one time-stepping scheme over the other. A comparative study of implicit and explicit time-stepping schemes is presented using an artificial two-material model. © 2023 The Authors. Proceedings in Applied Mathematics & Mechanics published by Wiley-VCH GmbH.

关键词： Stability criteria

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Exploring the Impact of Laser Drilling on Material Thermal Decomposition: A Computational Study Using KratosMultiphysics

Exploring the Impact of Laser Drilling on Material Thermal D...

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Thermal, Mechanical and Multiphysics Simulation and Experiments in Micro-Electronics and Micro-Systems EuroSimE

作者： Chongnan Peng Qi Tao Thomas Krivec Guillermo Casas Salvador Latorre Thomas Antretter Johannes Macher Peter Fuchs Polymer Competence Center Leoben GmbH Institute of Mechanics Montanuniversitaet Leoben Austria Technologie & Systemtechnik Aktiengesellschaft International Center for Numerical Methods in Engineering

Laser drilling has gained widespread popularity in industrial applications due to its precision, non-contact nature, speed, efficiency, and energy-saving attributes. This technology plays a vital role in the manufacturing of printed circuit boards (PCBs) and semiconductors. Additionally, femtosecond laser drilling has enhanced the capabilities of micro- and nano-fabrication of materials. The reliability of PCBs is heavily influenced by the laser drilling process. During laser drilling, numerous physical and chemical changes occur within a short timeframe, and the complexity of these changes remains a subject of ongoing investigation. Given the challenges of observing such rapid material transformations through experiments, simulation, and computational analysis offer a cost-effective alternative. KratosMultiphysics is a multi-physics solver employed to address a variety of process simulations across different fields. This paper initially gathered material parameters and recorded various test results under different laser drilling conditions for comparison with simulation outcomes. Utilizing KratosMultiphysics as a computational tool, we simulate the ablation of material with the subsequent heat conduction and decomposition of the polymer material according to a new numerical model.

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Implementation of Machine Learning Models for Predicting the Inactivation Performance of Escherichia Coli in Wastewater Through Varied Photo-Chemical Processes and Aqueous Matrix Combinations

Implementation of Machine Learning Models for Predicting the...

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International Conference on Wider-Uptake of Water Resource Recovery from Wastewater Treatment, ICWRR 2024

作者： Pascacio, P. Vicente, D.J. Salazar, F. Berruti, I. Nahim, S. Polo, M.I. Oller, I. CIMNE - International Centre for Numerical Methods in Engineering Madrid Spain Barcelona08034 Spain CIEMAT - Plataforma Solar de Almería Ctra. De Senés S/N Almería Tabernas04200 Spain CIESOL Joint Centre of the University of Almería-CIEMAT Almería04120 Spain

ISBN: (纸本)9783031633522

Despite the potential of sunlight-based Photo-chemical Processes (P-CPs) for bacterial inactivation in wastewater, their efficient design requires a delicate balance between optimal bacterial inactivation and the associated costs and time incurred in trial-based designs. To address this challenge, this study explores the implementation of four Machine Learning (ML) models to predict the inactivation performance of E. coli in wastewater across diverse P-CPs. The evaluation of the models demonstrated the usefulness of ML models in streamlining the design process and enhancing the effectiveness of P-CPs without the need for extensive experimental trials. Specifically, the Random Forest model presented the lowest Root Mean Squared Error (RMSE) (0.88) compared to XGBoost, Support Vector Machine (SVM), and Artificial Neural Network (ANN) with values of 1.03, 1.22, and 1.25, respectively. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

关键词： Escherichia coli

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Statistical considerations of corrosion initiation and propagation 2nd

Statistical considerations of corrosion initiation and propa...

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2nd Workshop on Capacity Assessment of Corroded Reinforced Concrete Structures, CACRCS DAYS 2020

作者： Andrade, Carmen Izquierdo, David CIMNE: International Center for Numerical Methods in Engineering Madrid Spain UPM: Politechnical University of Madrid Spain

ISBN: (纸本)9782940643103

Active corrosion initiates when the pH on the rebar surface decreases. This decrease is produced either by the arrival of the carbonation front or by the local depassivation due to the chloride attack. The progression of this corrosion would depend on several variables which are function of the variability of the material itself, of its aging with time and of the external climatic conditions. All of them produce an "intrinsic" variability which is necessary to be characterized for the accuracy of the predictions of service life. In the present communication, the statistical analysis made for the characterization of chloride threshold is discussed, as well as the spatial and temporal variability of the corrosion arte in real exposure conditions. © 2021, Fédération Internationale du Béton – International Federation for Structural Concrete.

关键词： Corrosion

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Advances in the description of corrosion induced cracking (Key-note lecture) 2nd

Advances in the description of corrosion induced cracking (K...

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2nd Workshop on Capacity Assessment of Corroded Reinforced Concrete Structures, CACRCS DAYS 2020

作者： Andrade, Carmen Anaya, Pablo CIMNE: International Center for Numerical Methods in Engineering-UPC Spain UPM-Politechnical University of Madrid Spain

ISBN: (纸本)9782940643103

The steps in the corrosion development from depassivation of the reinforcement until cracking of the concrete cover, has been studied mainly through computer simulations, although also some very interesting papers have been published on the steel/concrete interface in the preliminary steps of corrosion. In the lecture, based in new tests made by the authors on bond strength of wires, it will be presented some advances on the description of the corrosion processes progressively developed after corrosion initiation and which are the most accessible influencing factors. The parameters that whose calibration is described are: a) the oxide expansion, b) the rust bulk modulus, c) the "porous zone" thickness, d) the generated empty space of the incipient cracks in the diffusion of the oxides. © 2021, Fédération Internationale du Béton – International Federation for Structural Concrete.

关键词： Steel corrosion

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A DEEP LEARNING APPROACH FOR CURVATURE PREDICTION IN ALGEBRAIC VOLUME OF FLUID methods 9

A DEEP LEARNING APPROACH FOR CURVATURE PREDICTION IN ALGEBRA...

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9th International Conference on Computational methods for Coupled Problems in Science and engineering, COUPLED PROBLEMS 2021

作者： Kraus, Zacharias Friedrich, Jonas Köhler, Felix Schäfer, Michael Institute of Numerical Methods in Mechanical Engineering Technical University of Darmstadt Dolivostraße 15 Darmstadt64293 Germany

The accurate prediction of the curvature of fluid-fluid interfaces is crucial for appropriately modeling the surface forces when computing two-phase flows with immiscible fluids. The volume of fluid (VOF) method is often used for these computations to specify the different fluids and the interface by the so-called volume fraction field. In this study, a deep artificial neural network is trained to predict the interface curvature from the volume fraction values. This approach is investigated within an algebraic VOF framework. A rudimentary interface resharpening algorithm is introduced for the input stencils to enhance the accuracy and robustness when the interface can not be captured entirely sharp. The performance of different neural network architectures is evaluated by generic test data and the computation of two oscillating droplet flow configurations. © 2021 9th International Conference on Computational methods for Coupled Problems in Science and engineering, COUPLED PROBLEMS 2021. All rights reserved.

关键词： Volume fraction

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Documenting rock mass failure with UAV during an emergency phase: Castell de Mur case study 13

Documenting rock mass failure with UAV during an emergency p...

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13th Landslides and Engineered Slopes. Experience, Theory and Practice, ISL

作者： Roger, Ruiz-Carulla Corominas, Jordi CIMNE International Centre for Numerical Methods in Engineering Spain UPC Universitat Politècnica de Catalunya-BarcelonaTech Spain

The understanding of the conditioning factors and of the mechanisms involved in rockfalls are requirements for a successful risk assessment and for the prevention of future events. In that respect, the detailed documentation of past event may contribute to this goal. This communication presents methodologies based on UAV surveys to collect detailed documentation of a rock failure as fast as possible to allow the opening of the affected road. The Castell de Mur rock mass failure was a catastrophic mass movement involving around 18.000 m3 and causing 2 fatalities. We use this case to show the possibilities of immediate UAV surveys to create products and models to characterize and document a rock mass failure. The photogrammetric products (orthophoto, Digital Elevation Model, 3D Point cloud and 3D texturized mesh) are used to characterize the rock failure obtaining: high-resolution topographic maps;the block size distribution of fragments in the deposit;the total mobilized volume estimated;the distribution of rock bridges from scar image analysis;and finally, the identification of the involved joint sets and interpretation of the failure mechanism. These products may be used to characterize the failure and to identify the key features for subsequent stability analysis. The realization of the UAV flight has allowed us to collect detailed information about the failure scar and the rockfall debris that would otherwise have been lost after the clean-up of the site and implementation of the remedial works. © 2021 Landslides and Engineered Slopes. Experience, Theory and Practice

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numerical STUDY ON THE FLUID-STRUCTURE INTERACTION AND AERODYNAMIC NOISE RADIATION OF A MEMBRANE AIRFOIL 9

NUMERICAL STUDY ON THE FLUID-STRUCTURE INTERACTION AND AEROD...

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9th International Conference on Computational methods for Coupled Problems in Science and engineering, COUPLED PROBLEMS 2021

作者： Kolb, Elena Schäfer, Michael Institute of Numerical Methods in Mechanical Engineering Technische Universität Darmstadt Dolivostraße 15 Darmstadt64293 Germany

This paper investigates the fluid-structure interaction phenomena and their effect on the aerodynamic noise radiation observed for a membrane airfoil subjected to a turbulent flow at a fixed angle of attack α = 20° . For this purpose, two cases with different Reynolds numbers (Re = 53,100 and Re = 79,700) are simulated. The applied partitioned fluid-structure interaction approach uses large eddy simulations to predict the incompressible flow problem and includes geometric non-linear effects for the structural problem. Following a hybrid method based on a hydrodynamic/acoustic splitting technique, the incompressible flow field solution provides the acoustic source term for the aeroacoustic computation. The results suggest a coupling between the vortex shedding, the dynamic structural response and the radiated aerodynamic sound for this configuration. © 2021 9th International Conference on Computational methods for Coupled Problems in Science and engineering, COUPLED PROBLEMS 2021. All rights reserved.

关键词： Reynolds number

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