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Showing records 101 to 125 of 387. [First] Page: 1 2 3 4 5 6 7 8 9 Last
Development of Steady-State and Dynamic Mass-Energy Constrained Neural Networks using Noisy Transient Data
Angan Mukherjee, Debangsu Bhattacharyya
July 9, 2024 (v1)
Keywords: Energy Conservation, Equality Constraints, Forward Problem, Inverse Problem, Mass Conservation, Noisy Data
This paper presents the development of algorithms for mass-energy constrained neural network (MECNN) models that can exactly conserve the overall mass and energy of distributed chemical process systems, even though the noisy steady-state/transient data used for optimal model training violate the same. For developing dynamic mass-energy constrained network models for distributed systems, hybrid series and parallel dynamic-static neural networks are used as candidate architectures. The proposed approaches for solving both the inverse and forward problems are validated considering both steady-state and dynamic data in presence of various noise characteristics. The proposed network structures and algorithms are applied to the development of data-driven models of a nonlinear non-isothermal reactor that involves an exothermic reaction making it significantly challenging to exactly satisfy the mass and energy conservation laws of the system only by using the available input and output boundar... [more]
Fast, Accurate, and Robust Fault Detection and Diagnosis of Industrial Processes
Alireza Miraliakbar, Zheyu Jiang
July 9, 2024 (v1)
Keywords: Fault Detection and Diagnosis, Process Monitoring, Riemannian Manifold, Statistical Process Control, Support Vector Machine
Modern industrial processes are continuously monitored by a large number of sensors. Despite having access to large volumes of historical and online sensor data, industrial practitioners still face challenges in the era of Industry 4.0 in effectively utilizing them to perform online process monitoring and fast fault detection and diagnosis. To target these challenges, in this work, we present a novel framework named “FARM” for Fast, Accurate, and Robust online process Monitoring. FARM is a holistic monitoring framework that integrates (a) advanced multivariate statistical process control (SPC) for fast anomaly detection of nonparametric, heterogeneous data streams, and (b) modified support vector machine (SVM) for accurate and robust fault classification. Unlike existing general-purpose process monitoring frameworks, FARM’s unique hierarchical architecture decomposes process monitoring into two fault detection and diagnosis, each of which is conducted by targeted algorithms. Here, we t... [more]
Machine Learning-Aided Process Design for Microwave-Assisted Ammonia Production
Md Abdullah Al Masud, Alazar Araia, Yuxin Wang, Jianli Hu, Yuhe Tian
July 9, 2024 (v1)
Keywords: Ammonia Production, Machine Learning, Neural Networks, Process Design, Process Intensification
Machine learning (ML) has become a powerful tool to analyze complex relationships between multiple variables and to unravel valuable information from big datasets. However, an open research question lies in how ML can accelerate the design and optimization of processes in the early experimental development stages with limited data. In this work, we investigate the ML-aided process design of a microwave reactor for ammonia production with exceedingly little experimental data. We propose an integrated approach of synthetic minority oversampling technique (SMOTE) regression combined with neural networks to quantitatively design and optimize the microwave reactor. To address the limited data challenge, SMOTE is applied to generate synthetic data based on experimental data at different reaction conditions. Neural network has been demonstrated to effectively capture the nonlinear relationships between input features and target outputs. The softplus activation function is used for a smoother... [more]
Optimizing Batch Crystallization with Model-based Design of Experiments
Hailey G. Lynch, Aaron Bjarnason, Daniel J. Laky, Cameron J. Brown, Alexander W. Dowling
July 9, 2024 (v1)
Keywords: Batch Crystallization, Digital Twins, Intelligent Systems, Model-based Design, Pyomo
Adaptive and self-optimizing intelligent systems such as digital twins are increasingly important in science and engineering. Digital twins utilize mathematical models to provide added precision to decision-making. However, physics-informed models are challenging to build, calibrate, and validate with existing data science methods. Model-based design of experiments (MBDoE) is a popular framework for optimizing data collection to maximize parameter precision in mathematical models and digital twins. In this work, we apply MBDoE, facilitated by the open-source package Pyomo.DoE, to train and validate mathematical models for batch crystallization. We quantitatively examined the estimability of the model parameters for experiments with different cooling rates. This analysis provides a quantitative explanation for the heuristic of using multiple experiments at different cooling rates.
Learning Hybrid Extraction and Distillation using Phenomena-based String Representation
Jianping Li
July 9, 2024 (v1)
We present a string representation for hybrid extraction and distillation using symbols representing phenomena building blocks. Unlike the conventional equipment-based string representation, the proposed representation captures the design details of liquid-liquid extraction and distillation. We generate a set of samples through the procedure of input parameter sampling and superstructure optimization that minimizes separation cost. We convert these generated samples into a set of string representations based on pre-defined rules. We use these string representations as descriptors and connect them with conditional variational encoder. The trained conditional variational encoder shows good prediction accuracy. We further use the trained conditional variational encoder to screen designs of hybrid extraction and distillation with desired cost investment.
Exploring Quantum Optimization for Computer-aided Molecular and Process Design
Ashfaq Iftakher, M. M. Faruque Hasan
July 9, 2024 (v1)
Keywords: CAMPD, Multiscale Modelling, Optimization, Process Design, Quantum Optimization
Computer-aided Molecular and Process Design (CAMPD) is an equation-oriented multi-scale decision making framework for designing both materials (molecules) and processes for separation, reaction, and reactive separation whenever material choice significantly impacts process performance. The inherent nonlinearity and nonconvexity in CAMPD optimization models, introduced through the property and process models, pose challenges to state-of-the-art solvers. Recently, quantum computing (QC) has shown promise for solving complex optimization problems, especially those involving discrete decisions. This motivates us to explore the potential usage of quantum optimization techniques for solving CAMPD problems. We have developed a technique for directly solving a class of mixed integer nonlinear programs using QC. Our approach represents both continuous and integer design decisions by a set of binary variables through encoding schemes. This transformation allows to reformulate certain types of CA... [more]
Optimal Design of Antibody Extraction Systems using Protein A Resin with Multicycling
Fred Ghanem, Purnima M. Kodate, Gerard M. Capellades, Kirti M. Yenkie
July 9, 2024 (v1)
Subject: Biosystems
Antibody therapies are important in treating life-threatening ailments such as cancer and autoimmune diseases. Purity of the antibody is essential for successful applications and Protein A selective resin extraction is the standard step for antibody recovery. Unfortunately, such resins can cost up to 30% of the total cost of antibody production. Hence, the optimal design of this purification step becomes a critical factor in downstream processing to minimize the size of the column needed. An accurate predictive model, as a digital twin representing the purification process, is necessary where changes in the flow rates and the inlet concentrations are modeled via the Method of Moments. The system uncertainties are captured by including the stochastic Ito process model of Brownian motion with drift. Pontryagin’s Maximum Principle under uncertainty is then applied to predict the flowrate control strategy for optimized resin use, column design, and efficient capturing of the antibodies. In... [more]
Improving Mechanistic Model Accuracy with Machine Learning Informed Physics
William Farlessyost, Shweta Singh
July 9, 2024 (v1)
Machine learning presents opportunities to improve the scale-specific accuracy of mechanistic models in a data-driven manner. Here we demonstrate the use of a machine learning technique called Sparse Identification of Nonlinear Dynamics (SINDy) to improve a simple mechanistic model of algal growth. Time-series measurements of the microalga Chlorella Vulgaris were generated under controlled photobioreactor conditions at the University of Technology Sydney. A simple mechanistic growth model based on intensity of light and temperature was integrated over time and compared to the time-series data. While the mechanistic model broadly captured the overall growth trend, discrepancies remained between the model and data due to the model's simplicity and non-ideal behavior of real-world measurement. SINDy was applied to model the residual error by identifying an error derivative correction term. Addition of this SINDy-informed error dynamics term shows improvement to model accuracy while mainta... [more]
Neural Networks for Prediction of Complex Chemistry in Water Treatment Process Optimization
Alexander V. Dudchenko, Oluwamayowa O. Amusat
July 9, 2024 (v1)
Water chemistry plays a critical role in the design and operation of water treatment processes. Detailed chemistry modeling tools use a combination of advanced thermodynamic models and extensive databases to predict phase equilibria and reaction phenomena. The complexity and formulation of these models preclude their direct integration in equation-oriented modeling platforms, making it difficult to use their capabilities for rigorous water treatment process optimization. Neural networks (NN) can provide a pathway for integrating the predictive capability of chemistry software into equation-oriented models and enable optimization of complex water treatment processes across a broad range of conditions and process designs. Herein, we assess how NN architecture and training data impact their accuracy and use in equation-oriented water treatment models. We generate training data using PhreeqC software and determine how data generation and sample size impact the accuracy of trained NNs. The... [more]
Hybrid Rule-based and Optimization-driven Decision Framework for the Rapid Synthesis of End-to-End Optimal (E2EO) and Sustainable Pharmaceutical Manufacturing Flowsheets
Yash Barhate, Daniel Casas-Orozco, Daniel J. Laky, Gintaras V. Reklaitis, Zoltan K. Nagy
July 9, 2024 (v1)
Subject: Optimization
Keywords: Derivative-Free Optimization, Industry 40, Modelling and Simulations, Optimization, Process Synthesis
In this paper, a hybrid heuristic rule-based and deterministic optimization-driven process decision framework is presented for the analysis and optimization of process flowsheets for end-to-end optimal (E2E0) pharmaceutical manufacturing. The framework accommodates various operating modes, such as batch, semi-batch and continuous, for the different unit operations that implement each manufacturing step. To address the challenges associated with solving process synthesis problems using a simulation-optimization approach, heuristic-based process synthesis rules are employed to facilitate the reduction of the superstructure into smaller sub-structures that can be more readily optimized. The practical application of the framework is demonstrated through a case study involving the end-to-end continuous manufacturing of an anti-cancer drug, lomustine. Alternative flowsheet structures are evaluated in terms of the sustainability metric, E-factor while ensuring compliance with the required pro... [more]
Cost-optimal Selection of pH Control for Mineral Scaling Prevention in High Recovery Reverse Osmosis Desalination
Oluwamayowa O. Amusat, Alexander V. Dudchenko, Adam A. Atia, Timothy Bartholomew
July 9, 2024 (v1)
Keywords: Optimization, Pretreatment, Reverse Osmosis, Surrogate Model, Technoeconomic Analysis, Water
Explicitly incorporating the effects of chemical phenomena such as chemical pretreatment and mineral scaling during the design of treatment systems is critical; however, the complexity of these phenomena and limitations on data have historically hindered the incorporation of detailed water chemistry into the modeling and optimization of water desalination systems. Thus, while qualitative assessments and experimental studies on chemical pretreatment and scaling are abundant in the literature, very little has been done to assess the technoeconomic implications of different chemical pretreatment alternatives within the context of end-to-end water treatment train optimization. In this work, we begin to address this challenge by exploring the impact of pH control during pretreatment on the cost and operation of a high-recovery desalination train. We compare three pH control methods used in water treatment (H2SO4, HCl, and CO2) and assess their impact on the operation of a desalination plant... [more]
Learn-To-Design: Reinforcement Learning-Assisted Chemical Process Optimization
Eslam G. Al-Sakkari, Ahmed Ragab, Mohamed Ali, Hanane Dagdougui, Daria C. Boffito, Mouloud Amazouz
July 9, 2024 (v1)
Subject: Optimization
Keywords: Artificial Intelligence, Carbon Capture, Machine Learning, Optimization, Process Design, Reinforcement Learning, Simulation-based Optimization
This paper proposes an AI-assisted approach aimed at accelerating chemical process design through causal incremental reinforcement learning (CIRL) where an intelligent agent is interacting iteratively with a process simulation environment (e.g., Aspen HYSYS, DWSIM, etc.). The proposed approach is based on an incremental learnable optimizer capable of guiding multi-objective optimization towards optimal design variable configurations, depending on several factors including the problem complexity, selected RL algorithm and hyperparameters tuning. One advantage of this approach is that the agent-simulator interaction significantly reduces the vast search space of design variables, leading to an accelerated and optimized design process. This is a generic causal approach that enables the exploration of new process configurations and provides actionable insights to designers to improve not only the process design but also the design process across various applications. The approach was valid... [more]
A GRASP Heuristic for Solving an Acquisition Function Embedded in a Parallel Bayesian Optimization Framework
R. Cory Allen, Youngdae Kim, Dimitri J. Papageorgiou
July 9, 2024 (v1)
Subject: Optimization
Design problems for process systems engineering applications often require multi-scale modeling integrating detailed process models. Consequently, black-box optimization and surrogate modeling have continued to play a fundamental role in mission-critical design applications. Inherent in surrogate modeling applications, particularly those constrained by “expensive” function evaluations, are the questions of how to properly balance “exploration” and “exploitation” and how to do so while harnessing parallel computing in techniques. We devise and investigate a one-step look-ahead GRASP heuristic for balancing exploration and exploitation in a parallel environment. Computational results reveal that our approach can yield equivalent or superior surrogate quality with near linear scaling in the number of parallel samples.
Design of Plastic Waste Chemical Recycling Process Considering Uncertainty
Zhifei Yuliu, Yuqing Luo, Marianthi Ierapetritou
July 9, 2024 (v1)
Keywords: Design Under Uncertainty, Optimization, Plastic Waste, Polymers, Process Design, Technoeconomic Analysis
Chemical recycling of plastics is a promising technology to reduce carbon footprint and ease the pressure of waste treatment. Specifically, highly efficient conversion technologies for polyolefins will be the most effective solution to address the plastic waste crisis, given that polyolefins are the primary contributors to global plastic production. Significant challenges encountered by plastic waste valorization facilities include the uncertainty in the composition of the waste feedstock, process yield, and product price. These variabilities can lead to compromised performance or even render operations infeasible. To address these challenges, this work applied the robust optimization-based framework to design an integrated polyolefin chemical recycling plant. Data-driven surrogate model was built to capture the separation units’ behavior and reduce the computational complexity of the optimization problem. It was found that when process yield and price uncertainties were considered, wa... [more]
Optimal Design of Intensified Towers for CO2 Capture with Internal, Printed Heat Exchangers
Stephen Summits, Paul Akula, Debangsu Bhattacharyya, Grigorios Panagakos, Benjamin Omell, Michael Matuszewski
July 9, 2024 (v1)
Solvent-based carbon capture processes typically suffer from the temperature rise of the solvent due to the heat of absorption of CO2. This increased temperature is not thermodynamically favorable and results in a significant reduction in performance in the absorber column. As opposed to interstage coolers, which only remove, cool, and return the solvent at discrete locations in the column, internal coolers that are integrated with the packing can cool the process inline, which can result in improved efficiency. This work presents the modeling of these internal coolers within an existing generic, equation-oriented absorber column model that can cool the process while allowing for simultaneous mass transfer. Optimization of this model is also performed, which is capable of optimally choosing the best locations to place these devices, such that heat removal and mass transfer area are balanced. Results of the optimization have shown that optimally placed cooling elements result in a signi... [more]
A Study on Accelerated Convergence of Cyclic Steady State in Adsorption Process Simulations
Sai Gokul Subraveti, Kian Karimi, Matteo Gazzani, Rahul Anantharaman
July 9, 2024 (v1)
Keywords: acceleration methods, cyclic adsorption processes, Modelling, Optimization, process design
Cyclic adsorption processes attain a cyclic-steady state (CSS) condition by undergoing repeated cycles in time, owing to their transient and modular nature. Mathematically, solving a set of underlying nonlinear partial differential equations iteratively for different steps in a cycle until the CSS condition is attained presents a computational challenge, making the simulation and optimization of cyclic adsorption processes time-consuming. This paper focuses on expediting the CSS convergence in adsorption process simulations by implementing two vector-based acceleration methods that offer quadratic convergence akin to Newton’s methods. These methods are straightforward to implement, requiring no prior knowledge of the first derivatives (or Jacobian). The study demonstrates the efficacy of accelerated convergence by considering two adsorption processes that exhibit complex dynamics, namely, a four-step vacuum swing adsorption and a six-step temperature swing adsorption cycles for post-co... [more]
Optimal Design Approaches for Cost-Effective Manufacturing and Deployment of Chemical Process Families with Economies of Numbers
Georgia Stinchfield, Sherzoy Jan, Joshua C. Morgan, Miguel Zamarripa, Carl D. Laird
July 9, 2024 (v1)
Keywords: Carbon Capture, Energy Systems, Optimization, Process Design
Developing methods for rapid, large-scale deployment of carbon capture systems is critical for meeting climate change goals. Optimization-based decisions can be employed at the design and manufacturing phases to minimize the costs of deployment and operation. Manufacturing standardization results in significant cost savings due to economies of numbers. Building on previous work, we present a process family design approach to design a set of carbon capture systems while explicitly including economies of numbers savings within the formulation. Our formulation optimizes both the number and characteristics of the common components in the platform and simultaneously designs the resulting set of carbon capture systems. Savings from economies of numbers are explicitly included in the formulation to determine the number of components in the platform. We show and discuss the savings we gain from economies of numbers.
Recent Advances of PyROS: A Pyomo Solver for Nonconvex Two-Stage Robust Optimization in Process Systems Engineering
Jason A. F. Sherman, Natalie M. Isenberg, John D. Siirola, Chrysanthos E. Gounaris
July 9, 2024 (v1)
Subject: Optimization
In this work, we present recent algorithmic and implementation advances of the nonconvex two-stage robust optimization solver PyROS. Our advances include extensions of the scope of PyROS to models with uncertain variable bounds, improvements to the formulations and/or initializations of the various subproblems used by the underlying cutting set algorithm, and extensions to the pre-implemented uncertainty set interfaces. The effectiveness of PyROS is demonstrated through the results of an original benchmarking study on a library of over 8,500 small-scale instances, with variations in the nonlinearities, degree-of-freedom partitioning, uncertainty sets, and polynomial decision rule approximations. To demonstrate the utility of PyROS for large-scale process models, we present the results of a carbon capture case study. Overall, our results highlight the effectiveness of PyROS for obtaining robust solutions to optimization problems with uncertain equality constraints.
Design Space Identification of the Rotary Tablet Press
Mohammad Shahab, Sunidhi Bachawala, Marcial Gonzalez, Gintaras Reklaitis, Zoltan Nagy
July 9, 2024 (v1)
Keywords: design space, direct compression, Optimization, pharmaceutical process, tablet press
The determination of the design space (DS) in a pharmaceutical process is a crucial aspect of the quality-by-design (QbD) initiative which promotes quality built into the desired product. This is achieved through a deep understanding of how the critical quality attributes (CQAs) and process parameters (CPPs) interact that have been demonstrated to provide quality assurance. For computational inexpensive models, the original process model can be directly deployed to identify the design space. One such crucial process is the Tablet Press (TP), which directly compresses the powder blend into individual units of the final product or adds dry or wet granulation to meet specific formulation needs. In this work, we identify the design space of input variables in a TP such that there is a (probabilistic) guarantee that the tablets meet the quality constraints under a set of operating conditions. A reduced-order model of TP is assigned for this purpose where the effects of lubricants and glidan... [more]
Cybersecurity, Image-Based Control, and Process Design and Instrumentation Selection
Dominic Messina, Akkarakaran Francis Leonard, Ryan Hightower, Kip Nieman, Renee O’Neill, Paloma Beacham, Katie Tyrrell, Muhammad Adnan, Helen Durand
July 9, 2024 (v1)
Keywords: Cybersecurity, Dynamic Modelling, Image-Based Control, Industry 40, Instrumentation, Nonlinear Model Predictive Control, Simulation
Within an Industry 4.0 framework, a variety of new considerations are of increasing importance, such as securing processes against cyberattacks on the control systems or utilizing advances in image processing for image-based control. These new technologies impact relationships between process design and control. In this work, we discuss some of these potential relationships, beginning with a discussion of side channel attacks and what they suggest about ways of evaluating plant design and instrumentation selection, along with controller and security schemes, particularly as more data is collected and there is a move toward an industrial Internet of Things. Next, we highlight how the 3D computer graphics software tool set Blender can be utilized to analyze a variety of considerations related to ensuring safety of plant operation and facilitating the design of assemblies with image-based sensing.
Optimal Process Synthesis Implementing Phenomena-based Building Blocks and Structural Screening
David Krone, Erik Esche, Mirko Skiborowski, Jens-Uwe Repke
July 9, 2024 (v1)
Keywords: Distillation, Optimization, Phase Equilibria, Phenomena Building Block, Process Synthesis
Superstructure optimization for process synthesis is a challenging endeavour typically leading to large scale MINLP formulations. By the combination of phenomena-based building blocks, accurate thermodynamics, and structural screening we obtain a new framework for optimal process synthesis, which overcomes prior limitations regarding solution by deterministic MINLP solvers in combination with accurate thermodynamics. This is facilitated by MOSAICmodeling’s generic formulation of models in MathML / XML and subsequent decomposition and code export to GAMS and C++. A branch & bound algorithm is implemented to solve the overall MINLP problem, wherein the structural screening penalizes instances, which are deemed nonsensical and should not be further pursued. The general capabilities of this approach are shown for the distillation-based separation of a ternary system.
Adsorption-based Atmospheric Water Extraction Process: Kinetic Analysis and Stochastic Optimization
Jinsu Kim, Shubham Jamdade, Yanhui Yuan, Matthew J. Realff
July 9, 2024 (v1)
Subject: Optimization
Keywords: Atmospheric Water Extraction AWE, Kinetic Analysis, Metal-Organic Framework MOF, Meteorological Analysis, Two-stage Stochastic Programming TSSP
Adsorption-based Atmospheric Water Extraction (AWE) is an energy-efficient distributed freshwater supply method. This research focuses on AWE's kinetic analysis and stochastic optimization, investigating the impact of ambient conditions, kinetics, and weather variability. A one-dimensional fixed-bed system was numerically analyzed using the validated isotherm of MIL-100 (Fe), assuming different kinetic parameters within the linear driving force model. Stochastic optimization, based on annual weather data from Georgia (GA), illustrates the influence of weather conditions on AWE process performance, operation, and cost. Our study offers valuable insights for future research, including site selection, adsorbent material development, and process design. We outline three critical areas for further exploration: experimental verification, material screening, and meteorological site selection.
Beyond Yield: Assessing Reaction System Performance using Economics
Mary A. Katebah, Ma’moun Al-Rawashdeh, Patrick Linke
July 9, 2024 (v1)
Keywords: Propane, Reaction, Reaction Engineering, Technoeconomic Analysis
Early stage exploration of reaction systems, including catalyst selection, operating conditions’ specifications, reactor design, and optimization, is critical in the engineering field. It is general practice in the reaction engineering field to explore systems against certain performance metrics, of which yield is one of the most commonly utilized objectives. While the yield provides a quantitative measure of how efficiently reactants are converted into target product(s), its definition is ambiguous, particularly in the presence of side/ incomplete reactions, and multiple products. Most of the yield definitions focus on a specific target product; however, conditions within the reactor search space that provide a maximum yield for one product may not be the same as those for another. Moreover, the presence of other undesired products that are not considered may reduce the overall efficiency of the system. This necessitates the utilization of a more holistic metric that encompasses the v... [more]
Simultaneous Optimization of Design and Operating Conditions for RPB-based CO2 Capture Process
Howoun Jung, NohJin Park, Jay H. Lee
July 9, 2024 (v1)
Keywords: Carbon Dioxide Capture, Modelling and Simulations, Process Design, Process Intensification, Technoeconomic Analysis
Although global efforts for CO2 capture are underway, large-scale CO2 capture projects still face economic risks and technical challenges. The Rotating Packed Bed (RPB) provides an alternative solution by mitigating location constraints and enabling a gradual increase in the scale of CO2 capture through compact modular sizes. However, the main challenge in RPB-based CO2 capture processes lies in the limited experience with implementing industrial-scale RPB processes. The intricate relationship between RPB unit design, operating conditions, and process performance further complicates the process-level analysis for scale-up. To address these challenges, we propose an optimization-based process design for RPB-based CO2 capture. Leveraging rigorous process modeling and simulation, we aim to make simultaneous decisions on RPB unit design and operating conditions. Ultimately, our goal is to develop a cost-effective and optimal RPB-based CO2 capture process, supported by comprehensive cost ev... [more]
Integration of Design and Operation with Discretization Error Control
Christian Hoffmann, Erik Esche, Jens-Uwe Repke
July 9, 2024 (v1)
Keywords: Grid refinement, Integration of design and operation, Nonlinear programming, Process design
Optimization-based process design is a central task of process systems engineering. However, solely relying on steady-state models may potentially lead to dynamic constraint violations, hinder robust performance, or simply reduce the controllability of a process. This has led to the consideration of process dynamics in the design phase, which is commonly termed integration of design and operation / control. Recently, we proposed a framework to carry out this integrative task by formulating a large-scale nonlinear programming problem that is solved simultaneously. To this end, the dynamic process model was discretized, and dynamic variability and parametric uncertainty were included. However, the proposed framework only operates on constant lengths of the finite elements. The discretization error was not assessed. Within this contribution, a method for quantifying this discretization error and adapting the number of finite elements accordingly is incorporated into the recently proposed... [more]
Showing records 101 to 125 of 387. [First] Page: 1 2 3 4 5 6 7 8 9 Last