TY - JOUR A1 - Amani, Jafar A1 - Saboor Bagherzadeh, Amir A1 - Rabczuk, Timon T1 - Error estimate and adaptive refinement in mixed discrete least squares meshless method JF - Mathematical Problems in Engineering N2 - The node moving and multistage node enrichment adaptive refinement procedures are extended in mixed discrete least squares meshless (MDLSM) method for efficient analysis of elasticity problems. In the formulation of MDLSM method, mixed formulation is accepted to avoid second-order differentiation of shape functions and to obtain displacements and stresses simultaneously. In the refinement procedures, a robust error estimator based on the value of the least square residuals functional of the governing differential equations and its boundaries at nodal points is used which is inherently available from the MDLSM formulation and can efficiently identify the zones with higher numerical errors. The results are compared with the refinement procedures in the irreducible formulation of discrete least squares meshless (DLSM) method and show the accuracy and efficiency of the proposed procedures. Also, the comparison of the error norms and convergence rate show the fidelity of the proposed adaptive refinement procedures in the MDLSM method. KW - Elastizität KW - Fehlerabschätzung KW - MDLSM method Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170413-31181 ER - TY - JOUR A1 - Banihani, Suleiman A1 - Rabczuk, Timon A1 - Almomani, Thakir T1 - POD for real-time simulation of hyperelastic soft biological tissue using the point collocation method of finite spheres JF - Mathematical Problems in Engineering N2 - The point collocation method of finite spheres (PCMFS) is used to model the hyperelastic response of soft biological tissue in real time within the framework of virtual surgery simulation. The proper orthogonal decomposition (POD) model order reduction (MOR) technique was used to achieve reduced-order model of the problem, minimizing computational cost. The PCMFS is a physics-based meshfree numerical technique for real-time simulation of surgical procedures where the approximation functions are applied directly on the strong form of the boundary value problem without the need for integration, increasing computational efficiency. Since computational speed has a significant role in simulation of surgical procedures, the proposed technique was able to model realistic nonlinear behavior of organs in real time. Numerical results are shown to demonstrate the effectiveness of the new methodology through a comparison between full and reduced analyses for several nonlinear problems. It is shown that the proposed technique was able to achieve good agreement with the full model; moreover, the computational and data storage costs were significantly reduced. KW - Chirurgie KW - Finite-Elemente-Methode Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170413-31203 ER - TY - JOUR A1 - Chakraborty, Ayan A1 - Anitescu, Cosmin A1 - Zhuang, Xiaoying A1 - Rabczuk, Timon T1 - Domain adaptation based transfer learning approach for solving PDEs on complex geometries JF - Engineering with Computers N2 - In machine learning, if the training data is independently and identically distributed as the test data then a trained model can make an accurate predictions for new samples of data. Conventional machine learning has a strong dependence on massive amounts of training data which are domain specific to understand their latent patterns. In contrast, Domain adaptation and Transfer learning methods are sub-fields within machine learning that are concerned with solving the inescapable problem of insufficient training data by relaxing the domain dependence hypothesis. In this contribution, this issue has been addressed and by making a novel combination of both the methods we develop a computationally efficient and practical algorithm to solve boundary value problems based on nonlinear partial differential equations. We adopt a meshfree analysis framework to integrate the prevailing geometric modelling techniques based on NURBS and present an enhanced deep collocation approach that also plays an important role in the accuracy of solutions. We start with a brief introduction on how these methods expand upon this framework. We observe an excellent agreement between these methods and have shown that how fine-tuning a pre-trained network to a specialized domain may lead to an outstanding performance compare to the existing ones. As proof of concept, we illustrate the performance of our proposed model on several benchmark problems. KW - Maschinelles Lernen KW - NURBS KW - Transfer learning KW - Domain Adaptation KW - NURBS geometry KW - Navier–Stokes equations Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20220811-46776 UR - https://link.springer.com/article/10.1007/s00366-022-01661-2 VL - 2022 SP - 1 EP - 20 ER - TY - JOUR A1 - Faizollahzadeh Ardabili, Sina A1 - Najafi, Bahman A1 - Alizamir, Meysam A1 - Mosavi, Amir A1 - Shamshirband, Shahaboddin A1 - Rabczuk, Timon T1 - Using SVM-RSM and ELM-RSM Approaches for Optimizing the Production Process of Methyl and Ethyl Esters JF - Energies N2 - The production of a desired product needs an effective use of the experimental model. The present study proposes an extreme learning machine (ELM) and a support vector machine (SVM) integrated with the response surface methodology (RSM) to solve the complexity in optimization and prediction of the ethyl ester and methyl ester production process. The novel hybrid models of ELM-RSM and ELM-SVM are further used as a case study to estimate the yield of methyl and ethyl esters through a trans-esterification process from waste cooking oil (WCO) based on American Society for Testing and Materials (ASTM) standards. The results of the prediction phase were also compared with artificial neural networks (ANNs) and adaptive neuro-fuzzy inference system (ANFIS), which were recently developed by the second author of this study. Based on the results, an ELM with a correlation coefficient of 0.9815 and 0.9863 for methyl and ethyl esters, respectively, had a high estimation capability compared with that for SVM, ANNs, and ANFIS. Accordingly, the maximum production yield was obtained in the case of using ELM-RSM of 96.86% for ethyl ester at a temperature of 68.48 °C, a catalyst value of 1.15 wt. %, mixing intensity of 650.07 rpm, and an alcohol to oil molar ratio (A/O) of 5.77; for methyl ester, the production yield was 98.46% at a temperature of 67.62 °C, a catalyst value of 1.1 wt. %, mixing intensity of 709.42 rpm, and an A/O of 6.09. Therefore, ELM-RSM increased the production yield by 3.6% for ethyl ester and 3.1% for methyl ester, compared with those for the experimental data. KW - Biodiesel KW - Optimierung KW - extreme learning machine KW - machine learning KW - response surface methodology KW - support vector machine KW - OA-Publikationsfonds2018 Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20181025-38170 UR - https://www.mdpi.com/1996-1073/11/11/2889 IS - 11, 2889 SP - 1 EP - 20 PB - MDPI CY - Basel ER - TY - CHAP A1 - Ghorashi, Seyed Shahram A1 - Rabczuk, Timon A1 - Ródenas García, Juan José A1 - Lahmer, Tom ED - Gürlebeck, Klaus ED - Lahmer, Tom ED - Werner, Frank T1 - T-SPLINE BASED XIGA FOR ADAPTIVE MODELING OF CRACKED BODIES T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar N2 - Safety operation of important civil structures such as bridges can be estimated by using fracture analysis. Since the analytical methods are not capable of solving many complicated engineering problems, numerical methods have been increasingly adopted. In this paper, a part of isotropic material which contains a crack is considered as a partial model and the proposed model quality is evaluated. EXtended IsoGeometric Analysis (XIGA) is a new developed numerical approach [1, 2] which benefits from advantages of its origins: eXtended Finite Element Method (XFEM) and IsoGeometric Analysis (IGA). It is capable of simulating crack propagation problems with no remeshing necessity and capturing singular field at the crack tip by using the crack tip enrichment functions. Also, exact representation of geometry is possible using only few elements. XIGA has also been successfully applied for fracture analysis of cracked orthotropic bodies [3] and for simulation of curved cracks [4]. XIGA applies NURBS functions for both geometry description and solution field approximation. The drawback of NURBS functions is that local refinement cannot be defined regarding that it is based on tensorproduct constructs unless multiple patches are used which has also some limitations. In this contribution, the XIGA is further developed to make the local refinement feasible by using Tspline basis functions. Adopting a recovery based error estimator in the proposed approach for evaluation of the model quality and performing the adaptive processes is in progress. Finally, some numerical examples with available analytical solutions are investigated by the developed scheme. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Computerunterstütztes Verfahren Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27637 UR - http://euklid.bauing.uni-weimar.de/ikm2012 SN - 1611-4086 ER - TY - JOUR A1 - Guo, Hongwei A1 - Alajlan, Naif A1 - Zhuang, Xiaoying A1 - Rabczuk, Timon T1 - Physics-informed deep learning for three-dimensional transient heat transfer analysis of functionally graded materials JF - Computational Mechanics N2 - We present a physics-informed deep learning model for the transient heat transfer analysis of three-dimensional functionally graded materials (FGMs) employing a Runge–Kutta discrete time scheme. Firstly, the governing equation, associated boundary conditions and the initial condition for transient heat transfer analysis of FGMs with exponential material variations are presented. Then, the deep collocation method with the Runge–Kutta integration scheme for transient analysis is introduced. The prior physics that helps to generalize the physics-informed deep learning model is introduced by constraining the temperature variable with discrete time schemes and initial/boundary conditions. Further the fitted activation functions suitable for dynamic analysis are presented. Finally, we validate our approach through several numerical examples on FGMs with irregular shapes and a variety of boundary conditions. From numerical experiments, the predicted results with PIDL demonstrate well agreement with analytical solutions and other numerical methods in predicting of both temperature and flux distributions and can be adaptive to transient analysis of FGMs with different shapes, which can be the promising surrogate model in transient dynamic analysis. KW - Wärmeübergang KW - Deep Learning KW - Modellierung KW - physics-informed activation function KW - heat transfer KW - functionally graded materials Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20230517-63666 UR - https://link.springer.com/article/10.1007/s00466-023-02287-x VL - 2023 SP - 1 EP - 12 PB - Springer CY - Berlin ER - TY - JOUR A1 - Guo, Hongwei A1 - Zhuang, Xiaoying A1 - Chen, Pengwan A1 - Alajlan, Naif A1 - Rabczuk, Timon T1 - Analysis of three-dimensional potential problems in non-homogeneous media with physics-informed deep collocation method using material transfer learning and sensitivity analysis JF - Engineering with Computers N2 - In this work, we present a deep collocation method (DCM) for three-dimensional potential problems in non-homogeneous media. This approach utilizes a physics-informed neural network with material transfer learning reducing the solution of the non-homogeneous partial differential equations to an optimization problem. We tested different configurations of the physics-informed neural network including smooth activation functions, sampling methods for collocation points generation and combined optimizers. A material transfer learning technique is utilized for non-homogeneous media with different material gradations and parameters, which enhance the generality and robustness of the proposed method. In order to identify the most influential parameters of the network configuration, we carried out a global sensitivity analysis. Finally, we provide a convergence proof of our DCM. The approach is validated through several benchmark problems, also testing different material variations. KW - Deep learning KW - Kollokationsmethode KW - Collocation method KW - Potential problem KW - Activation function KW - Transfer learning Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20220811-46764 UR - https://link.springer.com/article/10.1007/s00366-022-01633-6 VL - 2022 SP - 1 EP - 22 ER - TY - JOUR A1 - Ilyani Akmar, A.B. A1 - Kramer, O. A1 - Rabczuk, Timon T1 - Multi-objective evolutionary optimization of sandwich structures: An evaluation by elitist non-dominated sorting evolution strategy JF - American Journal of Engineering and Applied Sciences N2 - In this study, an application of evolutionary multi-objective optimization algorithms on the optimization of sandwich structures is presented. The solution strategy is known as Elitist Non-Dominated Sorting Evolution Strategy (ENSES) wherein Evolution Strategies (ES) as Evolutionary Algorithm (EA) in the elitist Non-dominated Sorting Genetic algorithm (NSGA-II) procedure. Evolutionary algorithm seems a compatible approach to resolve multi-objective optimization problems because it is inspired by natural evolution, which closely linked to Artificial Intelligence (AI) techniques and elitism has shown an important factor for improving evolutionary multi-objective search. In order to evaluate the notion of performance by ENSES, the well-known study case of sandwich structures are reconsidered. For Case 1, the goals of the multi-objective optimization are minimization of the deflection and the weight of the sandwich structures. The length, the core and skin thicknesses are the design variables of Case 1. For Case 2, the objective functions are the fabrication cost, the beam weight and the end deflection of the sandwich structures. There are four design variables i.e., the weld height, the weld length, the beam depth and the beam width in Case 2. Numerical results are presented in terms of Paretooptimal solutions for both evaluated cases. KW - Optimierung KW - Stahlbau KW - Multi-objective Evolutionary Optimization, Elitist Non- Dominated Sorting Evolution Strategy (ENSES), Sandwich Structure, Pareto-Optimal Solutions, Evolutionary Algorithm Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170418-31402 SP - 185 EP - 201 ER - TY - JOUR A1 - Jiang, Jin-Wu A1 - Zhuang, Xiaoying A1 - Rabczuk, Timon T1 - Orientation dependent thermal conductance in single-layer MoS 2 JF - Scientific Reports N2 - We investigate the thermal conductivity in the armchair and zigzag MoS2 nanoribbons, by combining the non-equilibrium Green's function approach and the first-principles method. A strong orientation dependence is observed in the thermal conductivity. Particularly, the thermal conductivity for the armchair MoS2 nanoribbon is about 673.6 Wm−1 K−1 in the armchair nanoribbon, and 841.1 Wm−1 K−1 in the zigzag nanoribbon at room temperature. By calculating the Caroli transmission, we disclose the underlying mechanism for this strong orientation dependence to be the fewer phonon transport channels in the armchair MoS2 nanoribbon in the frequency range of [150, 200] cm−1. Through the scaling of the phonon dispersion, we further illustrate that the thermal conductivity calculated for the MoS2 nanoribbon is esentially in consistent with the superior thermal conductivity found for graphene. KW - Mechanische Eigenschaft KW - Wärmeleitfähigkeit KW - Nanoribbons, thermal conductivity Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170418-31417 ER - TY - JOUR A1 - Mortazavi, Bohayra A1 - Pereira, Luiz Felipe C. A1 - Jiang, Jin-Wu A1 - Rabczuk, Timon T1 - Modelling heat conduction in polycrystalline hexagonal boron-nitride films JF - Scientific Reports N2 - We conducted extensive molecular dynamics simulations to investigate the thermal conductivity of polycrystalline hexagonal boron-nitride (h-BN) films. To this aim, we constructed large atomistic models of polycrystalline h-BN sheets with random and uniform grain configuration. By performing equilibrium molecular dynamics (EMD) simulations, we investigated the influence of the average grain size on the thermal conductivity of polycrystalline h-BN films at various temperatures. Using the EMD results, we constructed finite element models of polycrystalline h-BN sheets to probe the thermal conductivity of samples with larger grain sizes. Our multiscale investigations not only provide a general viewpoint regarding the heat conduction in h-BN films but also propose that polycrystalline h-BN sheets present high thermal conductivity comparable to monocrystalline sheets. KW - Wärmeleitfähigkeit KW - Bornitrid KW - Finite-Elemente-Methode Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170425-31534 ER -