@inproceedings{GhorashiRabczukRodenasGarciaetal., author = {Ghorashi, Seyed Shahram and Rabczuk, Timon and R{\´o}denas Garc{\´i}a, Juan Jos{\´e} and Lahmer, Tom}, title = {T-SPLINE BASED XIGA FOR ADAPTIVE MODELING OF CRACKED BODIES}, series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar}, booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar}, editor = {G{\"u}rlebeck, Klaus and Lahmer, Tom and Werner, Frank}, organization = {Bauhaus-Universit{\"a}t Weimar}, issn = {1611-4086}, doi = {10.25643/bauhaus-universitaet.2763}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27637}, pages = {13}, abstract = {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.}, subject = {Angewandte Informatik}, language = {en} } @article{BanihaniRabczukAlmomani, author = {Banihani, Suleiman and Rabczuk, Timon and Almomani, Thakir}, title = {POD for real-time simulation of hyperelastic soft biological tissue using the point collocation method of finite spheres}, series = {Mathematical Problems in Engineering}, journal = {Mathematical Problems in Engineering}, doi = {10.1155/2013/386501}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170413-31203}, abstract = {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.}, subject = {Chirurgie}, language = {en} } @article{RabczukGuoZhuangetal., author = {Rabczuk, Timon and Guo, Hongwei and Zhuang, Xiaoying and Chen, Pengwan and Alajlan, Naif}, title = {Stochastic deep collocation method based on neural architecture search and transfer learning for heterogeneous porous media}, series = {Engineering with Computers}, volume = {2022}, journal = {Engineering with Computers}, publisher = {Springer}, address = {London}, doi = {10.1007/s00366-021-01586-2}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220209-45835}, pages = {1 -- 26}, abstract = {We present a stochastic deep collocation method (DCM) based on neural architecture search (NAS) and transfer learning for heterogeneous porous media. We first carry out a sensitivity analysis to determine the key hyper-parameters of the network to reduce the search space and subsequently employ hyper-parameter optimization to finally obtain the parameter values. The presented NAS based DCM also saves the weights and biases of the most favorable architectures, which is then used in the fine-tuning process. We also employ transfer learning techniques to drastically reduce the computational cost. The presented DCM is then applied to the stochastic analysis of heterogeneous porous material. Therefore, a three dimensional stochastic flow model is built providing a benchmark to the simulation of groundwater flow in highly heterogeneous aquifers. The performance of the presented NAS based DCM is verified in different dimensions using the method of manufactured solutions. We show that it significantly outperforms finite difference methods in both accuracy and computational cost.}, subject = {Maschinelles Lernen}, language = {en} } @article{ChakrabortyAnitescuZhuangetal., author = {Chakraborty, Ayan and Anitescu, Cosmin and Zhuang, Xiaoying and Rabczuk, Timon}, title = {Domain adaptation based transfer learning approach for solving PDEs on complex geometries}, series = {Engineering with Computers}, volume = {2022}, journal = {Engineering with Computers}, doi = {10.1007/s00366-022-01661-2}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220811-46776}, pages = {1 -- 20}, abstract = {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.}, subject = {Maschinelles Lernen}, language = {en} } @article{ShiraziMohebbiAzadiKakavandetal., author = {Shirazi, A. H. N. and Mohebbi, Farzad and Azadi Kakavand, M. R. and He, B. and Rabczuk, Timon}, title = {Paraffin Nanocomposites for Heat Management of Lithium-Ion Batteries: A Computational Investigation}, series = {JOURNAL OF NANOMATERIALS}, journal = {JOURNAL OF NANOMATERIALS}, doi = {10.1155/2016/2131946}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170411-31141}, abstract = {Lithium-ion (Li-ion) batteries are currently considered as vital components for advances in mobile technologies such as those in communications and transport. Nonetheless, Li-ion batteries suffer from temperature rises which sometimes lead to operational damages or may even cause fire. An appropriate solution to control the temperature changes during the operation of Li-ion batteries is to embed batteries inside a paraffin matrix to absorb and dissipate heat. In the present work, we aimed to investigate the possibility of making paraffin nanocomposites for better heat management of a Li-ion battery pack. To fulfill this aim, heat generation during a battery charging/discharging cycles was simulated using Newman's well established electrochemical pseudo-2D model. We couple this model to a 3D heat transfer model to predict the temperature evolution during the battery operation. In the later model, we considered different paraffin nanocomposites structures made by the addition of graphene, carbon nanotubes, and fullerene by assuming the same thermal conductivity for all fillers. This way, our results mainly correlate with the geometry of the fillers. Our results assess the degree of enhancement in heat dissipation of Li-ion batteries through the use of paraffin nanocomposites. Our results may be used as a guide for experimental set-ups to improve the heat management of Li-ion batteries.}, subject = {Batterie}, language = {en} } @article{IlyaniAkmarKramerRabczuk, author = {Ilyani Akmar, A.B. and Kramer, O. and Rabczuk, Timon}, title = {Multi-objective evolutionary optimization of sandwich structures: An evaluation by elitist non-dominated sorting evolution strategy}, series = {American Journal of Engineering and Applied Sciences}, journal = {American Journal of Engineering and Applied Sciences}, doi = {10.3844/ajeassp.2015.185.201}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170418-31402}, pages = {185 -- 201}, abstract = {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.}, subject = {Optimierung}, language = {en} } @article{MortazaviPereiraJiangetal., author = {Mortazavi, Bohayra and Pereira, Luiz Felipe C. and Jiang, Jin-Wu and Rabczuk, Timon}, title = {Modelling heat conduction in polycrystalline hexagonal boron-nitride films}, series = {Scientific Reports}, journal = {Scientific Reports}, doi = {10.1038/srep13228}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170425-31534}, abstract = {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.}, subject = {W{\"a}rmeleitf{\"a}higkeit}, language = {en} } @article{GuoZhuangChenetal., author = {Guo, Hongwei and Zhuang, Xiaoying and Chen, Pengwan and Alajlan, Naif and Rabczuk, Timon}, title = {Analysis of three-dimensional potential problems in non-homogeneous media with physics-informed deep collocation method using material transfer learning and sensitivity analysis}, series = {Engineering with Computers}, volume = {2022}, journal = {Engineering with Computers}, doi = {10.1007/s00366-022-01633-6}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220811-46764}, pages = {1 -- 22}, abstract = {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.}, subject = {Deep learning}, language = {en} } @article{ZhuangHuangLiangetal., author = {Zhuang, Xiaoying and Huang, Runqiu and Liang, Chao and Rabczuk, Timon}, title = {A coupled thermo-hydro-mechanical model of jointed hard rock for compressed air energy storage}, series = {Mathematical Problems in Engineering}, journal = {Mathematical Problems in Engineering}, doi = {10.1155/2014/179169}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170428-31726}, abstract = {Renewable energy resources such as wind and solar are intermittent, which causes instability when being connected to utility grid of electricity. Compressed air energy storage (CAES) provides an economic and technical viable solution to this problem by utilizing subsurface rock cavern to store the electricity generated by renewable energy in the form of compressed air. Though CAES has been used for over three decades, it is only restricted to salt rock or aquifers for air tightness reason. In this paper, the technical feasibility of utilizing hard rock for CAES is investigated by using a coupled thermo-hydro-mechanical (THM) modelling of nonisothermal gas flow. Governing equations are derived from the rules of energy balance, mass balance, and static equilibrium. Cyclic volumetric mass source and heat source models are applied to simulate the gas injection and production. Evaluation is carried out for intact rock and rock with discrete crack, respectively. In both cases, the heat and pressure losses using air mass control and supplementary air injection are compared.}, subject = {Energiespeicherung}, language = {en} } @article{AmaniSaboorBagherzadehRabczuk, author = {Amani, Jafar and Saboor Bagherzadeh, Amir and Rabczuk, Timon}, title = {Error estimate and adaptive refinement in mixed discrete least squares meshless method}, series = {Mathematical Problems in Engineering}, journal = {Mathematical Problems in Engineering}, doi = {10.1155/2014/721240}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170413-31181}, abstract = {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.}, subject = {Elastizit{\"a}t}, language = {en} }