K. Mattsson, T. Dao, Gustav Eriksson, Vidar Stiernström
It is well-known that higher-order methods (as compared to lower order accurate methods) capture transient phenomena more efficiently since they allow for a considerable reduction in the degrees of freedom for a given error tolerance. In particular, high-order finite difference methods (HOFDMs) are ideally suited for problems of this type, cf. the pioneering paper by Kreiss and Oliger [5]. For long-time simulations, it is imperative to use finite difference approximations that do not allow growth in time if the PDE does not allow growth—a property termed time stability [3]. Achieving time-stable HOFDM has received considerable past attention. A robust and well-proven high-order finite difference methodology, for well-posed initial boundary value problems (IBVP), is to combine summation-by-parts (SBP) operators [4, 6] and either the simultaneous approximation term (SAT) method [1], or the projection method [7] to impose boundary conditions.
{"title":"A hybrid adaptive method for initial-boundary value problems","authors":"K. Mattsson, T. Dao, Gustav Eriksson, Vidar Stiernström","doi":"10.23967/admos.2023.057","DOIUrl":"https://doi.org/10.23967/admos.2023.057","url":null,"abstract":"It is well-known that higher-order methods (as compared to lower order accurate methods) capture transient phenomena more efficiently since they allow for a considerable reduction in the degrees of freedom for a given error tolerance. In particular, high-order finite difference methods (HOFDMs) are ideally suited for problems of this type, cf. the pioneering paper by Kreiss and Oliger [5]. For long-time simulations, it is imperative to use finite difference approximations that do not allow growth in time if the PDE does not allow growth—a property termed time stability [3]. Achieving time-stable HOFDM has received considerable past attention. A robust and well-proven high-order finite difference methodology, for well-posed initial boundary value problems (IBVP), is to combine summation-by-parts (SBP) operators [4, 6] and either the simultaneous approximation term (SAT) method [1], or the projection method [7] to impose boundary conditions.","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127123133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Error Assessment for an Adaptive Finite Elements - Neural Networks Approach Applied to Parametric PDEs","authors":"A. Caboussat, M. Girardin, M. Picasso","doi":"10.23967/admos.2023.047","DOIUrl":"https://doi.org/10.23967/admos.2023.047","url":null,"abstract":"","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127843742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Parabolic partial differential equations (PDEs) with small random input data appear in a wide range of physical and real-world applications, for instance, in glaciology. In this work, we propose and analyze residual-based a posteriori error estimates for such equations in the L 2 P (Ω; L ∞ (0 , T ; L 2 ( D )))-norm, where (Ω , F , P ) is a complete probability space, D is the physical domain, T > 0 is the final time. To this end, we apply the perturbation technique to deal with uncertainty [2019, Arch. Comput. Methods Eng., 26, pp. 1313-1377]. In view of this technique, solving a PDE with small random input data is equivalent to solving decoupled deterministic problems. To approximate solution for these problems, we employ finite element method for the physical space approximation and backward Euler time-stepping scheme for time discretization. To obtain optimality in space, we employ the elliptic reconstruction operator [2003, SIAM J. Numer. Anal., 41, pp. 1585-1594]. The results could be seen as a generalization of the work presented in [2006, Math. Comput., 75, pp. 1627-1658] for the deterministic parabolic PDEs to the parabolic PDE with small uncertainties. Numerical investigations confirm the theoretical findings.
具有小随机输入数据的抛物型偏微分方程(PDEs)广泛出现在物理和现实世界的应用中，例如冰川学。在这项工作中，我们提出并分析了基于残差的后验误差估计在l2 P (Ω;L∞(0,t;L 2 (D)))-范数，其中(Ω， F, P)为完全概率空间，D为物理域，T > 0为最终时间。为此，我们应用摄动技术来处理不确定性[2019,Arch。第一版。Eng方法。书刊，26，第1313-1377页]。鉴于这种技术，求解具有小随机输入数据的PDE等价于求解解耦的确定性问题。为了逼近这些问题的解，我们采用有限元法进行物理空间逼近，并采用向后欧拉时间步进格式进行时间离散。为了获得空间上的最优性，我们使用椭圆重构算子[2003,SIAM J. number]。分析的， 41，第1585-1594页]。这些结果可以被看作是对[2006,Math]中提出的工作的概括。第一版。确定性抛物型偏微分方程与小不确定性抛物型偏微分方程的比较[j]。数值研究证实了理论结果。
{"title":"Elliptic reconstruction and a posteriori error estimates for the parabolic partial differential equations with small random input data","authors":"N. Shravani, G. Reddy","doi":"10.23967/admos.2023.028","DOIUrl":"https://doi.org/10.23967/admos.2023.028","url":null,"abstract":"Parabolic partial differential equations (PDEs) with small random input data appear in a wide range of physical and real-world applications, for instance, in glaciology. In this work, we propose and analyze residual-based a posteriori error estimates for such equations in the L 2 P (Ω; L ∞ (0 , T ; L 2 ( D )))-norm, where (Ω , F , P ) is a complete probability space, D is the physical domain, T > 0 is the final time. To this end, we apply the perturbation technique to deal with uncertainty [2019, Arch. Comput. Methods Eng., 26, pp. 1313-1377]. In view of this technique, solving a PDE with small random input data is equivalent to solving decoupled deterministic problems. To approximate solution for these problems, we employ finite element method for the physical space approximation and backward Euler time-stepping scheme for time discretization. To obtain optimality in space, we employ the elliptic reconstruction operator [2003, SIAM J. Numer. Anal., 41, pp. 1585-1594]. The results could be seen as a generalization of the work presented in [2006, Math. Comput., 75, pp. 1627-1658] for the deterministic parabolic PDEs to the parabolic PDE with small uncertainties. Numerical investigations confirm the theoretical findings.","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122503951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
L. Alvarez-Vázquez, N. García-Chan, A. Martínez, C. Rodríguez, M. Vázquez-Méndez
{"title":"Towards a More Efficient Evacuation of Crowds by Means of an Optimal Location of Exit Doors","authors":"L. Alvarez-Vázquez, N. García-Chan, A. Martínez, C. Rodríguez, M. Vázquez-Méndez","doi":"10.23967/admos.2023.015","DOIUrl":"https://doi.org/10.23967/admos.2023.015","url":null,"abstract":"","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115743199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Error Estimation for the Material Point and Particle in Cell Methods","authors":"M. Berzins","doi":"10.23967/admos.2023.046","DOIUrl":"https://doi.org/10.23967/admos.2023.046","url":null,"abstract":"","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"157 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113987929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Real-time monitoring of a system may be difficult when associated phenomena are multiphysics and multiscale. Difficulties mainly come from the numerical complexity which requires large computing resources that are hardly compatible with real-time.To overcome this issue, the initial high-fidelity parameterized physical model can be simplified, which leads to additional model bias. Moreover, parameter values can be inaccurate and erroneous. All those errors affect the effectiveness of numerical diagnosis and prognosis, and thus have to be corrected with assimilation techniques on observation data. Therefore, the monitoring of the process is made of two stages: (1) state estimation at the acquisition time, which may be associated with the identification of a set of unknown parameters of the parameterized model and the data-based enrichment of the model; (2) state prediction for future time steps from the updated model. The present study aims at implementing this framework with an extension, for time-dependent problems, of the Parameterized Background Data-Weak (PBDW) method introduced in [1]. Classical PBDW is a non-intrusive, reduced basis, real-time and in-situ data assimilation method that applies to physical systems modeled by parametrized pdes (initially for steady-state problems). The key idea of the formulation is to seek an approximation to the true state employing projection-by-data
{"title":"Real-time monitoring of additive manufacturing processes using a variational data assimilation method with model reduction and bias correction","authors":"L. Chamoin, W. Haik, Y. Maday","doi":"10.23967/admos.2023.017","DOIUrl":"https://doi.org/10.23967/admos.2023.017","url":null,"abstract":"Real-time monitoring of a system may be difficult when associated phenomena are multiphysics and multiscale. Difficulties mainly come from the numerical complexity which requires large computing resources that are hardly compatible with real-time.To overcome this issue, the initial high-fidelity parameterized physical model can be simplified, which leads to additional model bias. Moreover, parameter values can be inaccurate and erroneous. All those errors affect the effectiveness of numerical diagnosis and prognosis, and thus have to be corrected with assimilation techniques on observation data. Therefore, the monitoring of the process is made of two stages: (1) state estimation at the acquisition time, which may be associated with the identification of a set of unknown parameters of the parameterized model and the data-based enrichment of the model; (2) state prediction for future time steps from the updated model. The present study aims at implementing this framework with an extension, for time-dependent problems, of the Parameterized Background Data-Weak (PBDW) method introduced in [1]. Classical PBDW is a non-intrusive, reduced basis, real-time and in-situ data assimilation method that applies to physical systems modeled by parametrized pdes (initially for steady-state problems). The key idea of the formulation is to seek an approximation to the true state employing projection-by-data","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115014052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
N. Ta, L. Chamoin, A. Barbarulo, G. Puel, B. Faure
{"title":"An Adaptive Trefftz Method to Analyze the Influence of the Midfield Propagation Conditions on Environmental Railway Noise","authors":"N. Ta, L. Chamoin, A. Barbarulo, G. Puel, B. Faure","doi":"10.23967/admos.2023.049","DOIUrl":"https://doi.org/10.23967/admos.2023.049","url":null,"abstract":"","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122547898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Thanks to the significant advances in data sciences and numerical algorithms, and face to the current industrial and societal challenges, Physically-based data-driven computational modeling would have an important role in simulations based design for the development of innovative materials and new products. With the new paradigm of data Driven Computational Mechanics proposed by [1], the constitutive laws can be directly replaced by a collection of experimental data avoiding thus the crucial step of proposing a mathematical model that best fit the experiments and calibrating its inherent parameters. The DDCM bypasses the empirical constitutive laws and searches the solution as a double distance minimizing problem between the physical space (respecting thus the physical universal laws) and the material data manifold (discrete set of data points with no explicit mathematical model). Despite the recent applications of DDCM algorithms in numerical simulations, their practical using still remains limited to reversible behaviors and their extension to irreversible dissipation problems needs further developments. Moreover, the data generation phase needs more efforts to reduce its high (numerical or experimental) cost. We propose in this study a strategy that makes the most of Reduced Order Models (ROM) and Data Driven Computational Modeling (DDCM) to extend such a free material paradigm to more complicated problems, namely irreversible and multi-scale simulations. The application of the ”ROM+DDCM” framework will be illustrated for a 2D elasto-plastic problem and 3D multiscale thermal simulations. A tangent space based double distance algorithm is adopted for the DDCM [2] algorithm and the HOPGD [3] method is used for the ROM step.
{"title":"A \"ROM+DDCM\" framework for thermo-mechanical simulations","authors":"N. Blal, A. Gravouil","doi":"10.23967/admos.2023.025","DOIUrl":"https://doi.org/10.23967/admos.2023.025","url":null,"abstract":"Thanks to the significant advances in data sciences and numerical algorithms, and face to the current industrial and societal challenges, Physically-based data-driven computational modeling would have an important role in simulations based design for the development of innovative materials and new products. With the new paradigm of data Driven Computational Mechanics proposed by [1], the constitutive laws can be directly replaced by a collection of experimental data avoiding thus the crucial step of proposing a mathematical model that best fit the experiments and calibrating its inherent parameters. The DDCM bypasses the empirical constitutive laws and searches the solution as a double distance minimizing problem between the physical space (respecting thus the physical universal laws) and the material data manifold (discrete set of data points with no explicit mathematical model). Despite the recent applications of DDCM algorithms in numerical simulations, their practical using still remains limited to reversible behaviors and their extension to irreversible dissipation problems needs further developments. Moreover, the data generation phase needs more efforts to reduce its high (numerical or experimental) cost. We propose in this study a strategy that makes the most of Reduced Order Models (ROM) and Data Driven Computational Modeling (DDCM) to extend such a free material paradigm to more complicated problems, namely irreversible and multi-scale simulations. The application of the ”ROM+DDCM” framework will be illustrated for a 2D elasto-plastic problem and 3D multiscale thermal simulations. A tangent space based double distance algorithm is adopted for the DDCM [2] algorithm and the HOPGD [3] method is used for the ROM step.","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127824522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This contribution presents a combined framework to perform parametric surrogate modeling of vibroacoustic problems that enables efficient training of large-scale problems. The proposed framework combines the active subspace method to perform dimensionality reduction of high-dimensional problems and thereafter a clustering-based approach within the identified active subspace region to yield smaller training clusters. Finally, a trained neural network assists the cluster classification task for any desired parameter point so as to query the parametric system response during the online phase.
{"title":"Clustering-based Parametric Surrogate Modeling of Vibroacoustic Problems Assisted by Neural Networks and Active Subspace Method","authors":"H. Sreekumar, L. Outzen, U. Römer, S. Langer","doi":"10.23967/admos.2023.009","DOIUrl":"https://doi.org/10.23967/admos.2023.009","url":null,"abstract":"This contribution presents a combined framework to perform parametric surrogate modeling of vibroacoustic problems that enables efficient training of large-scale problems. The proposed framework combines the active subspace method to perform dimensionality reduction of high-dimensional problems and thereafter a clustering-based approach within the identified active subspace region to yield smaller training clusters. Finally, a trained neural network assists the cluster classification task for any desired parameter point so as to query the parametric system response during the online phase.","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130730133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: There are numerous challenges in generating high-quality meshes of cardiac anatomies due to the complex geometry of the heart, its curvature, and its motion. More generally, computational modeling of anatomical models bounded by curved surfaces can benefit from the use of high-order curved meshes. Using such meshes ensures that the curvature is captured correctly in the corresponding mesh. In addition, for a fixed level of accuracy, pairing a high-order mesh with a high-order PDE solver requires fewer mesh elements hence making the mesh generation and PDE solve much less computationally expensive. The use of high-order meshes in dynamic simulations helps prevent instabilities. In this talk, we first present our advancing front-based high-order tetrahedral mesh generation method for finite element meshes. While most existing high-order mesh generation methods employ a computer-aided design (CAD) model to represent the boundary surface, our method requires only the element vertices and connectivities. Thus, it can employ a high-order surface mesh which was generated from medical image segmentation masks or a CAD model. Our method then directly generates a high-order volume mesh and applies mesh optimization to utilize the higher degrees of freedom and further improve the mesh quality. Second, we present our high-order mesh warping algorithm for tetrahedral meshes, which allows us to perform time-dependent deformations present in biomedical applications. Our method is based on a finite element formulation for hyperelastic materials. We employ the two-parameter incompressible Mooney-Rivlin model with appropriate material properties to represent the continuum model. We use Newton iteration to solve the nonlinear elasticity equations obtained from the Mooney-Rivlin model and equilibrium conditions; the solution to the nonlinear elasticity equations then yields the deformed mesh. Finally, we use our methods to generate several second-order tetrahedral meshes of anatomical models obtained from medical images and CAD models and apply several time-dependent deformations. We conclude with a vision for research in mesh generation for biomedical simulation.
{"title":"High-Order Mesh Generation and Warping for Biomedical Simulations","authors":"Suzanne Shontz","doi":"10.23967/admos.2023.082","DOIUrl":"https://doi.org/10.23967/admos.2023.082","url":null,"abstract":": There are numerous challenges in generating high-quality meshes of cardiac anatomies due to the complex geometry of the heart, its curvature, and its motion. More generally, computational modeling of anatomical models bounded by curved surfaces can benefit from the use of high-order curved meshes. Using such meshes ensures that the curvature is captured correctly in the corresponding mesh. In addition, for a fixed level of accuracy, pairing a high-order mesh with a high-order PDE solver requires fewer mesh elements hence making the mesh generation and PDE solve much less computationally expensive. The use of high-order meshes in dynamic simulations helps prevent instabilities. In this talk, we first present our advancing front-based high-order tetrahedral mesh generation method for finite element meshes. While most existing high-order mesh generation methods employ a computer-aided design (CAD) model to represent the boundary surface, our method requires only the element vertices and connectivities. Thus, it can employ a high-order surface mesh which was generated from medical image segmentation masks or a CAD model. Our method then directly generates a high-order volume mesh and applies mesh optimization to utilize the higher degrees of freedom and further improve the mesh quality. Second, we present our high-order mesh warping algorithm for tetrahedral meshes, which allows us to perform time-dependent deformations present in biomedical applications. Our method is based on a finite element formulation for hyperelastic materials. We employ the two-parameter incompressible Mooney-Rivlin model with appropriate material properties to represent the continuum model. We use Newton iteration to solve the nonlinear elasticity equations obtained from the Mooney-Rivlin model and equilibrium conditions; the solution to the nonlinear elasticity equations then yields the deformed mesh. Finally, we use our methods to generate several second-order tetrahedral meshes of anatomical models obtained from medical images and CAD models and apply several time-dependent deformations. We conclude with a vision for research in mesh generation for biomedical simulation.","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"140 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132661885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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