Pub Date : 2021-09-21DOI: 10.1186/s40323-021-00205-5
Ghnatios, Chady, Barasinski, Anais
A nonparametric method assessing the error and variability margins in solutions depicted in a separated form using experimental results is illustrated in this work. The method assess the total variability of the solution including the modeling error and the truncation error when experimental results are available. The illustrated method is based on the use of the PGD separated form solutions, enriched by transforming a part of the PGD basis vectors into probabilistic one. The constructed probabilistic vectors are restricted to the physical solution’s Stiefel manifold. The result is a real-time parametric PGD solution enhanced with the solution variability and the confidence intervals.
{"title":"A nonparametric probabilistic method to enhance PGD solutions with data-driven approach, application to the automated tape placement process","authors":"Ghnatios, Chady, Barasinski, Anais","doi":"10.1186/s40323-021-00205-5","DOIUrl":"https://doi.org/10.1186/s40323-021-00205-5","url":null,"abstract":"A nonparametric method assessing the error and variability margins in solutions depicted in a separated form using experimental results is illustrated in this work. The method assess the total variability of the solution including the modeling error and the truncation error when experimental results are available. The illustrated method is based on the use of the PGD separated form solutions, enriched by transforming a part of the PGD basis vectors into probabilistic one. The constructed probabilistic vectors are restricted to the physical solution’s Stiefel manifold. The result is a real-time parametric PGD solution enhanced with the solution variability and the confidence intervals.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"30 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138510034","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}
Pub Date : 2021-09-04DOI: 10.1186/s40323-021-00203-7
Schein, Alexander, Gee, Michael W.
This work proposes a framework for projection-based model order reduction (MOR) of computational models aiming at a mechanical analysis of abdominal aortic aneurysms (AAAs). The underlying full-order model (FOM) is patient-specific, stationary and nonlinear. The quantities of interest are the von Mises stress and the von Mises strain field in the AAA wall, which result from loading the structure to the level of diastolic blood pressure at a fixed, imaged geometry (prestressing stage) and subsequent loading to the level of systolic blood pressure with associated deformation of the structure (deformation stage). Prestressing is performed with the modified updated Lagrangian formulation (MULF) approach. The proposed framework aims at a reduction of the computational cost in a many-query context resulting from model uncertainties in two material and one geometric parameter. We apply projection-based MOR to the MULF prestressing stage, which has not been presented to date. Additionally, we propose a reduced-order basis construction technique combining the concept of subspace angles and greedy maximin distance sampling. To further achieve computational speedup, the reduced-order model (ROM) is equipped with the energy-conserving mesh sampling and weighting hyper reduction method. Accuracy of the ROM is numerically tested in terms of the quantities of interest within given bounds of the parameter domain and performance of the proposed ROM in the many-query context is demonstrated by comparing ROM and FOM statistics built from Monte Carlo sampling for three different patient-specific AAAs.
{"title":"Greedy maximin distance sampling based model order reduction of prestressed and parametrized abdominal aortic aneurysms","authors":"Schein, Alexander, Gee, Michael W.","doi":"10.1186/s40323-021-00203-7","DOIUrl":"https://doi.org/10.1186/s40323-021-00203-7","url":null,"abstract":"This work proposes a framework for projection-based model order reduction (MOR) of computational models aiming at a mechanical analysis of abdominal aortic aneurysms (AAAs). The underlying full-order model (FOM) is patient-specific, stationary and nonlinear. The quantities of interest are the von Mises stress and the von Mises strain field in the AAA wall, which result from loading the structure to the level of diastolic blood pressure at a fixed, imaged geometry (prestressing stage) and subsequent loading to the level of systolic blood pressure with associated deformation of the structure (deformation stage). Prestressing is performed with the modified updated Lagrangian formulation (MULF) approach. The proposed framework aims at a reduction of the computational cost in a many-query context resulting from model uncertainties in two material and one geometric parameter. We apply projection-based MOR to the MULF prestressing stage, which has not been presented to date. Additionally, we propose a reduced-order basis construction technique combining the concept of subspace angles and greedy maximin distance sampling. To further achieve computational speedup, the reduced-order model (ROM) is equipped with the energy-conserving mesh sampling and weighting hyper reduction method. Accuracy of the ROM is numerically tested in terms of the quantities of interest within given bounds of the parameter domain and performance of the proposed ROM in the many-query context is demonstrated by comparing ROM and FOM statistics built from Monte Carlo sampling for three different patient-specific AAAs.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"31 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138510049","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}
Pub Date : 2021-09-04DOI: 10.1186/s40323-021-00204-6
M. Zahid, Khalid S. Syed
{"title":"Investigation of pollutants formation in a diesel engine using numerical simulation","authors":"M. Zahid, Khalid S. Syed","doi":"10.1186/s40323-021-00204-6","DOIUrl":"https://doi.org/10.1186/s40323-021-00204-6","url":null,"abstract":"","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42203236","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}
Pub Date : 2021-08-04DOI: 10.1186/s40323-021-00202-8
Chevreuil, Mathilde, Slama, Myriam
The paper deals with approximations of periodic functions that play a significant role in harmonic analysis. The approach revisits the trigonometric polynomials, seen as combinations of functions, and proposes to extend the class of models of the combined functions to a wider class of functions. The key here is to use structured functions, that have low complexity, with suitable functional representation and adapted parametrizations for the approximation. Such representation enables to approximate multivariate functions with few eventually random samples. The new parametrization is determined automatically with a greedy procedure, and a low rank format is used for the approximation associated with each new parametrization. A supervised learning algorithm is used for the approximation of a function of multiple random variables in tree-based tensor format, here the particular Tensor Train format. Adaptive strategies using statistical error estimates are proposed for the selection of the underlying tensor bases and the ranks for the Tensor-Train format. The method is applied for the estimation of the wall pressure for a flow over a cylinder for a range of low to medium Reynolds numbers for which we observe two flow regimes: a laminar flow with periodic vortex shedding and a laminar boundary layer with a turbulent wake (sub-critic regime). The automatic re-parametrization enables here to take into account the specific periodic feature of the pressure.
{"title":"A generalized Fourier transform by means of change of variables within multilinear approximation","authors":"Chevreuil, Mathilde, Slama, Myriam","doi":"10.1186/s40323-021-00202-8","DOIUrl":"https://doi.org/10.1186/s40323-021-00202-8","url":null,"abstract":"The paper deals with approximations of periodic functions that play a significant role in harmonic analysis. The approach revisits the trigonometric polynomials, seen as combinations of functions, and proposes to extend the class of models of the combined functions to a wider class of functions. The key here is to use structured functions, that have low complexity, with suitable functional representation and adapted parametrizations for the approximation. Such representation enables to approximate multivariate functions with few eventually random samples. The new parametrization is determined automatically with a greedy procedure, and a low rank format is used for the approximation associated with each new parametrization. A supervised learning algorithm is used for the approximation of a function of multiple random variables in tree-based tensor format, here the particular Tensor Train format. Adaptive strategies using statistical error estimates are proposed for the selection of the underlying tensor bases and the ranks for the Tensor-Train format. The method is applied for the estimation of the wall pressure for a flow over a cylinder for a range of low to medium Reynolds numbers for which we observe two flow regimes: a laminar flow with periodic vortex shedding and a laminar boundary layer with a turbulent wake (sub-critic regime). The automatic re-parametrization enables here to take into account the specific periodic feature of the pressure.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138510050","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}
Pub Date : 2021-07-27DOI: 10.1186/s40323-021-00201-9
J. Nitzler, C. Meier, K. W. Müller, W. Wall, N. Hodge
{"title":"A novel physics-based and data-supported microstructure model for part-scale simulation of laser powder bed fusion of Ti-6Al-4V","authors":"J. Nitzler, C. Meier, K. W. Müller, W. Wall, N. Hodge","doi":"10.1186/s40323-021-00201-9","DOIUrl":"https://doi.org/10.1186/s40323-021-00201-9","url":null,"abstract":"","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s40323-021-00201-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65853401","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}
Pub Date : 2021-07-23DOI: 10.1186/s40323-021-00209-1
Sebastian D. Proell, W. Wall, C. Meier
{"title":"A simple yet consistent constitutive law and mortar-based layer coupling schemes for thermomechanical macroscale simulations of metal additive manufacturing processes","authors":"Sebastian D. Proell, W. Wall, C. Meier","doi":"10.1186/s40323-021-00209-1","DOIUrl":"https://doi.org/10.1186/s40323-021-00209-1","url":null,"abstract":"","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"8 1","pages":"1-37"},"PeriodicalIF":0.0,"publicationDate":"2021-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48581605","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}
Pub Date : 2021-06-29DOI: 10.21203/rs.3.rs-651030/v1
E. S. Shoukralla, Nermin Saber, A. Y. Sayed
In this study, we applied an advanced barycentric Lagrange interpolation formula to find the interpolate solutions of weakly singular Fredholm integral equations of the second kind. The kernel is interpolated twice concerning both variables and then is transformed into the product of five matrices; two of them are monomial basis matrices. To isolate the singularity of the kernel, we developed two techniques based on a good choice of different two sets of nodes to be distributed over the integration domain. Each set is specific to one of the kernel arguments so that the kernel values never become zero or imaginary. The significant advantage of thetwo presented techniques is the ability to gain access to an algebraic linear system equivalent to the interpolant solution without applying the collocation method. Moreover, the convergence in the mean of the interpolant solution and the maximum error norm estimation are studied. The interpolate solutions of the illustrated four examples are found strongly converging uniformly to the exact solutions.
{"title":"Computational method for solving weakly singular Fredholm integral equations of the second kind using an advanced barycentric Lagrange interpolation formula","authors":"E. S. Shoukralla, Nermin Saber, A. Y. Sayed","doi":"10.21203/rs.3.rs-651030/v1","DOIUrl":"https://doi.org/10.21203/rs.3.rs-651030/v1","url":null,"abstract":"In this study, we applied an advanced barycentric Lagrange interpolation formula to find the interpolate solutions of weakly singular Fredholm integral equations of the second kind. The kernel is interpolated twice concerning both variables and then is transformed into the product of five matrices; two of them are monomial basis matrices. To isolate the singularity of the kernel, we developed two techniques based on a good choice of different two sets of nodes to be distributed over the integration domain. Each set is specific to one of the kernel arguments so that the kernel values never become zero or imaginary. The significant advantage of thetwo presented techniques is the ability to gain access to an algebraic linear system equivalent to the interpolant solution without applying the collocation method. Moreover, the convergence in the mean of the interpolant solution and the maximum error norm estimation are studied. The interpolate solutions of the illustrated four examples are found strongly converging uniformly to the exact solutions.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"8 1","pages":"1-22"},"PeriodicalIF":0.0,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43464520","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}
Pub Date : 2021-06-28DOI: 10.1186/s40323-021-00200-w
Sebastian L. Fuchs, Christoph Meier, Wolfgang A. Wall, Christian J. Cyron
The present work proposes an approach for fluid–solid and contact interaction problems including thermo-mechanical coupling and reversible phase transitions. The solid field is assumed to consist of several arbitrarily-shaped, undeformable but mobile rigid bodies, that are evolved in time individually and allowed to get into mechanical contact with each other. The fluid field generally consists of multiple liquid or gas phases. All fields are spatially discretized using the method of smoothed particle hydrodynamics (SPH). This approach is especially suitable in the context of continually changing interface topologies and dynamic phase transitions without the need for additional methodological and computational effort for interface tracking as compared to mesh- or grid-based methods. Proposing a concept for the parallelization of the computational framework, in particular concerning a computationally efficient evaluation of rigid body motion, is an essential part of this work. Finally, the accuracy and robustness of the proposed framework is demonstrated by several numerical examples in two and three dimensions, involving multiple rigid bodies, two-phase flow, and reversible phase transitions, with a focus on two potential application scenarios in the fields of engineering and biomechanics: powder bed fusion additive manufacturing (PBFAM) and disintegration of food boluses in the human stomach. The efficiency of the parallel computational framework is demonstrated by a strong scaling analysis.
{"title":"An SPH framework for fluid–solid and contact interaction problems including thermo-mechanical coupling and reversible phase transitions","authors":"Sebastian L. Fuchs, Christoph Meier, Wolfgang A. Wall, Christian J. Cyron","doi":"10.1186/s40323-021-00200-w","DOIUrl":"https://doi.org/10.1186/s40323-021-00200-w","url":null,"abstract":"The present work proposes an approach for fluid–solid and contact interaction problems including thermo-mechanical coupling and reversible phase transitions. The solid field is assumed to consist of several arbitrarily-shaped, undeformable but mobile rigid bodies, that are evolved in time individually and allowed to get into mechanical contact with each other. The fluid field generally consists of multiple liquid or gas phases. All fields are spatially discretized using the method of smoothed particle hydrodynamics (SPH). This approach is especially suitable in the context of continually changing interface topologies and dynamic phase transitions without the need for additional methodological and computational effort for interface tracking as compared to mesh- or grid-based methods. Proposing a concept for the parallelization of the computational framework, in particular concerning a computationally efficient evaluation of rigid body motion, is an essential part of this work. Finally, the accuracy and robustness of the proposed framework is demonstrated by several numerical examples in two and three dimensions, involving multiple rigid bodies, two-phase flow, and reversible phase transitions, with a focus on two potential application scenarios in the fields of engineering and biomechanics: powder bed fusion additive manufacturing (PBFAM) and disintegration of food boluses in the human stomach. The efficiency of the parallel computational framework is demonstrated by a strong scaling analysis.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"30 18","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138510031","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}
Pub Date : 2021-06-17DOI: 10.1186/s40323-021-00213-5
Zhe Bai, Liqian Peng
{"title":"Non-intrusive nonlinear model reduction via machine learning approximations to low-dimensional operators","authors":"Zhe Bai, Liqian Peng","doi":"10.1186/s40323-021-00213-5","DOIUrl":"https://doi.org/10.1186/s40323-021-00213-5","url":null,"abstract":"","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41324551","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}
Pub Date : 2021-06-04DOI: 10.1186/s40323-021-00199-0
Maialen Areitioaurtena, Unai Segurajauregi, Ville Akujärvi, Martin Fisk, Iker Urresti, Eneko Ukar
The numerical simulation of the induction heating process can be computationally expensive, especially if ferromagnetic materials are studied. There are several analytical models that describe the electromagnetic phenomena. However, these are very limited by the geometry of the coil and the workpiece. Thus, the usual method for computing more complex systems is to use the finite element method to solve the set of equations in the multiphysical system, but this easily becomes very time consuming. This paper deals with the problem of solving a coupled electromagnetic - thermal problem with higher computational efficiency. For this purpose, a semi-analytical modeling strategy is proposed, that is based on an initial finite element computation, followed by the use of analytical electromagnetic equations to solve the coupled electromagnetic-thermal problem. The usage of the simplified model is restricted to simple geometrical features such as flat or curved surfaces with great curvature to skin depth ratio. Numerical and experimental validation of the model show an average error between 0.9% and 4.1% in the prediction of the temperature evolution, reaching a greater accuracy than other analyzed commercial softwares. A 3D case of a double-row large size ball bearing is also presented, fully validating the proposed approach in terms of computational time and accuracy for complex industrial cases.
{"title":"A semi-analytical coupled simulation approach for induction heating","authors":"Maialen Areitioaurtena, Unai Segurajauregi, Ville Akujärvi, Martin Fisk, Iker Urresti, Eneko Ukar","doi":"10.1186/s40323-021-00199-0","DOIUrl":"https://doi.org/10.1186/s40323-021-00199-0","url":null,"abstract":"The numerical simulation of the induction heating process can be computationally expensive, especially if ferromagnetic materials are studied. There are several analytical models that describe the electromagnetic phenomena. However, these are very limited by the geometry of the coil and the workpiece. Thus, the usual method for computing more complex systems is to use the finite element method to solve the set of equations in the multiphysical system, but this easily becomes very time consuming. This paper deals with the problem of solving a coupled electromagnetic - thermal problem with higher computational efficiency. For this purpose, a semi-analytical modeling strategy is proposed, that is based on an initial finite element computation, followed by the use of analytical electromagnetic equations to solve the coupled electromagnetic-thermal problem. The usage of the simplified model is restricted to simple geometrical features such as flat or curved surfaces with great curvature to skin depth ratio. Numerical and experimental validation of the model show an average error between 0.9% and 4.1% in the prediction of the temperature evolution, reaching a greater accuracy than other analyzed commercial softwares. A 3D case of a double-row large size ball bearing is also presented, fully validating the proposed approach in terms of computational time and accuracy for complex industrial cases.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"30 23","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138510051","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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