A port-reduced static condensation reduced basis element method for large component-synthesized structures: approximation and A Posteriori error estimation

Background: We consider a static condensation reduced basis element framework for efficient approximation of parameter-dependent linear elliptic partial differential equations in large three-dimensional component-based domains. The approach features an offline computational stage in which a library of interoperable parametrized components is prepared; and an online computational stage in which these component archetypes may be instantiated and connected through predefined ports to form a global synthesized system. Thanks to the component-interior reduced basis approximations, the online computation time is often relatively small compared to a classical finite element calculation. Methods: In addition to reduced basis approximation in the component interiors, we employ in this paper port reduction with empirical port modes to reduce the number of degrees of freedom on the ports and thus the size of the Schur complement system. The framework is equipped with efficiently computable a posteriori error estimators that provide asymptotically rigorous bounds on the error in the approximation with respect to the underlying finite element discretization. We extend our earlier approach for two-dimensional scalar problems to the more demanding three-dimensional vector-field case. Results and Conclusions: This paper focuses on linear elasticity analysis for large structures with tens of millions of finite element degrees of freedom. Through our procedure we effectively reduce the number of degrees of freedom to a few thousand, and we demonstrate through extensive numerical results for a microtruss structure that our approach provides an accurate, rapid, and a posteriori verifiable approximation for relevant large-scale engineering problems.Research Council of NorwayUnited States. Office of Naval Research (ONR Grant N00014-11-0713

Port reduction in parametrized component static condensation: approximation and a posteriori error estimation

We introduce a port (interface) approximation and a posteriori error bound framework for a general component-based static condensation method in the context of parameter-dependent linear elliptic partial differential equations. The key ingredients are as follows: (i) efficient empirical port approximation spaces—the dimensions of these spaces may be chosen small to reduce the computational cost associated with formation and solution of the static condensation system; and (ii) a computationally tractable a posteriori error bound realized through a non-conforming approximation and associated conditioner—the error in the global system approximation, or in a scalar output quantity, may be bounded relatively sharply with respect to the underlying finite element discretization. Our approximation and a posteriori error bound framework is of particular computational relevance for the static condensation reduced basis element (SCRBE) method. We provide several numerical examples within the SCRBE context, which serve to demonstrate the convergence rate of our port approximation procedure as well as the efficacy of our port reduction error bounds.Research Council of NorwayUnited States. Office of Naval Research (Grant N00014-11-0713

Goats are able to adapt to virtual fencing; A field study in commercial goat herds on Norwegian farms

publishedVersio

Interleukin-8 is the single most up-regulated gene in whole genome profiling of H. pylori exposed gastric epithelial cells

<p>Abstract</p> <p>Background</p> <p>The association between <it>Helicobacter pylori </it>infection and upper gastrointestinal disease is well established. However, only a small fraction of <it>H. pylori </it>carriers develop disease, and there are great geographical differences in disease penetrance. The explanation to this enigma lies in the interaction between the bacterium and the host. <it>H. pylori </it>Outer Membrane Phospholipase A (OMPLA) has been suggested to play a role in the virulence of this bacterium. The aim of this study was to profile the most significant cellular pathways and biological processes affected in gastric epithelial cells during 24 h of <it>H. pylori </it>exposure, and to study the inflammatory response to OMPLA⁺and OMPLA^-<it>H. pylori </it>variants.</p> <p>Results</p> <p>Interleukin-8 was the most significantly up-regulated gene and appears to play a paramount role in the epithelial cell response to <it>H. pylori </it>infection and in the pathological processes leading to gastric disease. MAPK and NF-kappaB cellular pathways were powerfully activated, but did not seem to explain the impressive <it>IL-8 </it>response. There was marked up-regulation of <it>TP53BP2</it>, whose corresponding protein ASPP2 may interact with <it>H. pylori </it>CagA and cause marked p53 suppression of apoptosis. Other regulators of apoptosis also showed abberant regulation. We also identified up-regulation of several oncogenes and down-regulation of tumor suppressor genes as early as during the first 24 h of infection. <it>H. pylori </it>OMPLA phase variation did not seem to influence the inflammatory epithelial cell gene response in this experiment.</p> <p>Conclusion</p> <p>In whole genome analysis of the epithelial response to <it>H. pylori </it>exposure, <it>IL-8 </it>demonstrated the most marked up-regulation, and was involved in many of the most important cellular response processes to the infection. There was dysregulation of apoptosis, tumor suppressor genes and oncogenes as early as in the first 24 h of <it>H. pylori </it>infection, which may represent early signs of gastric tumorigenesis. OMPLA^+/-did not affect the acute inflammatory response to <it>H. pylori</it>.</p

Proper Generalized Decomposition solutions within a Domain Decomposition strategy

"This is the peer reviewed version of the following article: Huerta, Antonio, Enrique Nadal, and Francisco Chinesta. 2018. Proper Generalized Decomposition Solutions within a Domain Decomposition Strategy. International Journal for Numerical Methods in Engineering 113 (13). Wiley: 1972 94. doi:10.1002/nme.5729, which has been published in final form at https://doi.org/10.1002/nme.5729. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."[EN] Domain decomposition strategies and proper generalized decomposition are efficiently combined to obtain a fast evaluation of the solution approximation in parameterized elliptic problems with complex geometries. The classical difficulties associated to the combination of layered domains with arbitrarily oriented midsurfaces, which may require in-plane-out-of-plane techniques, are now dismissed. More generally, solutions on large domains can now be confronted within a domain decomposition approach. This is done with a reduced cost in the offline phase because the proper generalized decomposition gives an explicit description of the solution in each subdomain in terms of the solution at the interface. Thus, the evaluation of the approximation in each subdomain is a simple function evaluation given the interface values (and the other problem parameters). The interface solution can be characterized by any a priori user-defined approximation. Here, for illustration purposes, hierarchical polynomials are used. The repetitiveness of the subdomains is exploited to reduce drastically the offline computational effort. The online phase requires solving a nonlinear problem to determine all the interface solutions. However, this problem only has degrees of freedom on the interfaces and the Jacobian matrix is explicitly determined. Obviously, other parameters characterizing the solution (material constants, external loads, and geometry) can also be incorporated in the explicit description of the solution.European Commission, Grant/Award Number: MSCA ITN-ETN 675919; ESI group, Grant/Award Number: ENSAM ESI Chair; Spanish Ministry of Economy and Competitiveness, Grant/Award Number: DPI2017-85139-C2-2-R; Generalitat de Catalunya, Grant/Award Number: 2014SGR1471Huerta, A.; Nadal, E.; Chinesta Soria, FJ. (2018). Proper Generalized Decomposition solutions within a Domain Decomposition strategy. International Journal for Numerical Methods in Engineering. 113(13):1972-1994. https://doi.org/10.1002/nme.5729S1972199411313Ammar, A., Mokdad, B., Chinesta, F., & Keunings, R. (2006). A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. Journal of Non-Newtonian Fluid Mechanics, 139(3), 153-176. doi:10.1016/j.jnnfm.2006.07.007Chinesta, F., Leygue, A., Bordeu, F., Aguado, J. V., Cueto, E., Gonzalez, D., … Huerta, A. (2013). PGD-Based Computational Vademecum for Efficient Design, Optimization and Control. Archives of Computational Methods in Engineering, 20(1), 31-59. doi:10.1007/s11831-013-9080-xChinesta, F., Cueto, E., & Huerta, A. (2014). PGD for solving multidimensional and parametric models. CISM International Centre for Mechanical Sciences, 27-89. doi:10.1007/978-3-7091-1794-1_2Chinesta, F., Keunings, R., & Leygue, A. (2014). The Proper Generalized Decomposition for Advanced Numerical Simulations. SpringerBriefs in Applied Sciences and Technology. doi:10.1007/978-3-319-02865-1González, D., Ammar, A., Chinesta, F., & Cueto, E. (2009). Recent advances on the use of separated representations. International Journal for Numerical Methods in Engineering, n/a-n/a. doi:10.1002/nme.2710Ghnatios, C., Chinesta, F., & Binetruy, C. (2013). 3D Modeling of squeeze flows occurring in composite laminates. International Journal of Material Forming, 8(1), 73-83. doi:10.1007/s12289-013-1149-4Bognet, B., Bordeu, F., Chinesta, F., Leygue, A., & Poitou, A. (2012). Advanced simulation of models defined in plate geometries: 3D solutions with 2D computational complexity. Computer Methods in Applied Mechanics and Engineering, 201-204, 1-12. doi:10.1016/j.cma.2011.08.025Bognet, B., Leygue, A., & Chinesta, F. (2014). Separated representations of 3D elastic solutions in shell geometries. Advanced Modeling and Simulation in Engineering Sciences, 1(1), 4. doi:10.1186/2213-7467-1-4Ibáñez, R., Abisset-Chavanne, E., Chinesta, F., & Huerta, A. (2016). Simulating squeeze flows in multiaxial laminates: towards fully 3D mixed formulations. International Journal of Material Forming, 10(5), 653-669. doi:10.1007/s12289-016-1309-4Toselli, A., & Widlund, O. B. (2005). Domain Decomposition Methods — Algorithms and Theory. Springer Series in Computational Mathematics. doi:10.1007/b137868Dolean, V., Jolivet, P., & Nataf, F. (2015). An Introduction to Domain Decomposition Methods. doi:10.1137/1.9781611974065Nazeer, S. M., Bordeu, F., Leygue, A., & Chinesta, F. (2014). Arlequin based PGD domain decomposition. Computational Mechanics, 54(5), 1175-1190. doi:10.1007/s00466-014-1048-7Krause, R. H., & Wohlmuth, B. I. (2002). A Dirichlet-Neumann type algorithm for contact problems with friction. Computing and Visualization in Science, 5(3), 139-148. doi:10.1007/s00791-002-0096-2Farhat, C., & Roux, F.-X. (1991). A method of finite element tearing and interconnecting and its parallel solution algorithm. International Journal for Numerical Methods in Engineering, 32(6), 1205-1227. doi:10.1002/nme.1620320604Nitsche, J. (1971). Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 36(1), 9-15. doi:10.1007/bf02995904Freud J Stenberg R On weakly imposed boundary conditions for second order problems 1995 Venice, ItalyStenberg, R. (1995). On some techniques for approximating boundary conditions in the finite element method. Journal of Computational and Applied Mathematics, 63(1-3), 139-148. doi:10.1016/0377-0427(95)00057-7Becker, R., Hansbo, P., & Stenberg, R. (2003). A finite element method for domain decomposition with non-matching grids. ESAIM: Mathematical Modelling and Numerical Analysis, 37(2), 209-225. doi:10.1051/m2an:2003023Iapichino, L., Quarteroni, A., & Rozza, G. (2012). A reduced basis hybrid method for the coupling of parametrized domains represented by fluidic networks. Computer Methods in Applied Mechanics and Engineering, 221-222, 63-82. doi:10.1016/j.cma.2012.02.005Eftang, J. L., & Patera, A. T. (2013). Port reduction in parametrized component static condensation: approximation and a posteriori error estimation. International Journal for Numerical Methods in Engineering, 96(5), 269-302. doi:10.1002/nme.4543Eftang, J. L., & Patera, A. T. (2014). A port-reduced static condensation reduced basis element method for large component-synthesized structures: approximation and A Posteriori error estimation. Advanced Modeling and Simulation in Engineering Sciences, 1(1), 3. doi:10.1186/2213-7467-1-3Vallaghé, S., & Patera, A. T. (2014). The Static Condensation Reduced Basis Element Method for a Mixed-Mean Conjugate Heat Exchanger Model. SIAM Journal on Scientific Computing, 36(3), B294-B320. doi:10.1137/120887709Martini, I., Rozza, G., & Haasdonk, B. (2014). Reduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system. Advances in Computational Mathematics, 41(5), 1131-1157. doi:10.1007/s10444-014-9396-6Smetana, K. (2015). A new certification framework for the port reduced static condensation reduced basis element method. Computer Methods in Applied Mechanics and Engineering, 283, 352-383. doi:10.1016/j.cma.2014.09.020Smetana, K., & Patera, A. T. (2016). Optimal Local Approximation Spaces for Component-Based Static Condensation Procedures. SIAM Journal on Scientific Computing, 38(5), A3318-A3356. doi:10.1137/15m1009603Iapichino, L., Quarteroni, A., & Rozza, G. (2016). Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries. Computers & Mathematics with Applications, 71(1), 408-430. doi:10.1016/j.camwa.2015.12.001Maday, Y., & Rønquist, E. M. (2002). Journal of Scientific Computing, 17(1/4), 447-459. doi:10.1023/a:1015197908587Phuong Huynh, D. B., Knezevic, D. J., & Patera, A. T. (2012). A Static condensation Reduced Basis Element method : approximation anda posteriorierror estimation. ESAIM: Mathematical Modelling and Numerical Analysis, 47(1), 213-251. doi:10.1051/m2an/2012022Ammar, A., Huerta, A., Chinesta, F., Cueto, E., & Leygue, A. (2014). Parametric solutions involving geometry: A step towards efficient shape optimization. Computer Methods in Applied Mechanics and Engineering, 268, 178-193. doi:10.1016/j.cma.2013.09.003Zlotnik, S., Díez, P., Modesto, D., & Huerta, A. (2015). Proper generalized decomposition of a geometrically parametrized heat problem with geophysical applications. International Journal for Numerical Methods in Engineering, 103(10), 737-758. doi:10.1002/nme.4909Montlaur, A., Fernandez‐Mendez, S., & Huerta, A. (2008). Discontinuous Galerkin methods for the Stokes equations using divergence‐free approximations. International Journal for Numerical Methods in Fluids, 57(9), 1071-1092. doi:10.1002/fld.1716Ciarlet, P. G. (2002). The Finite Element Method for Elliptic Problems. doi:10.1137/1.9780898719208Szabó, B., & Babuška, I. (2011). Introduction to Finite Element Analysis. doi:10.1002/9781119993834Rozza G Fundamentals of reduced basis method for problems governed by parametrized PDEs and applications Separated Representations and PGD-Based Model Reduction CISM International Centre for Mechanical Sciences: Courses and Lectures 554 Vienna Springer 2014 153 227Ammar, A., Chinesta, F., Diez, P., & Huerta, A. (2010). An error estimator for separated representations of highly multidimensional models. Computer Methods in Applied Mechanics and Engineering, 199(25-28), 1872-1880. doi:10.1016/j.cma.2010.02.012Maday, Y., & Ronquist, E. M. (2004). The Reduced Basis Element Method: Application to a Thermal Fin Problem. SIAM Journal on Scientific Computing, 26(1), 240-258. doi:10.1137/s106482750241993

Approximation of Parametric Derivatives by the Empirical Interpolation Method

We introduce a general a priori convergence result for the approximation of parametric derivatives of parametrized functions. We consider the best approximations to parametric derivatives in a sequence of approximation spaces generated by a general approximation scheme, and we show that these approximations are convergent provided that the best approximation to the function itself is convergent. We also provide estimates for the convergence rates. We present numerical results with spaces generated by a particular approximation scheme—the Empirical Interpolation Method—to confirm the validity of the general theory

The Relationship Between Gambling Problems and the Five-Factor Model of Personality: A Systematic Review and Meta-Analysis

Objectives: The aim of the present meta-analysis was to synthesize results from the association between problem gambling (PG) and dimensions of the five factor model of personality and to identify potential moderators (gambling diagnosis: yes/no, comorbidity: yes/no and trait assessment: four or fewer items vs. five items or more) of these associations in meta-regressions. Methods: Searches were conducted in six databases; Medline, Web of Science, PsychInfo, Google Scholar, OpenGrey, and Cochrane Library (conducted on February, 22, 2021). Included studies: (1) reported a relationship between PG and at least one of the personality traits in the five-factor model, (2) contained information of zero-order correlations or sufficient data for such calculations, and (3) were original articles published in any European language. Case-studies, qualitative studies, and reviews were excluded. All articles were independently screened by two authors. Final agreement was reached through discussion or by consulting a third author. Risk of bias of the included studies was assessed by the Newcastle-Ottawa Scale. Data were synthesized using a random effects model. Results: In total 28 studies, comprising 20,587 participants, were included. The correlations between PG and the traits were as follows: Neuroticism: 0.273 (95% CI = 0.182, 0.358), conscientiousness −0.296 (95% CI = −0.400, −0.185), agreeableness −0.163 (95% CI = −0.223, −0.101), openness −0.219 (95% CI = −0.308, −0.127), and extroversion −0.083 (95% CI = −0.120, −0.046). For all meta-analyses the between study heterogeneity was significant. Presence of gambling diagnosis was the only moderator that significantly explained between-study variance showing a more negative correlation to extroversion when participants had a gambling diagnosis compared to when this was not the case. Discussion: The results indicated some publication bias. Correcting for this by a trim-and-fill procedure showed however that the findings were consistent. Clinicians and researchers should be aware of the associations between personality traits and PG. Previous studies have for example showed neuroticism to be related to treatment relapse, low scores on conscientiousness to predict treatment drop-out and agreeableness to reduce risk of treatment drop-out.publishedVersio

Heat flow and calculus on metric measure spaces with Ricci curvature bounded below - the compact case

We provide a quick overview of various calculus tools and of the main results concerning the heat flow on compact metric measure spaces, with applications to spaces with lower Ricci curvature bounds. Topics include the Hopf-Lax semigroup and the Hamilton-Jacobi equation in metric spaces, a new approach to differentiation and to the theory of Sobolev spaces over metric measure spaces, the equivalence of the L^2-gradient flow of a suitably defined "Dirichlet energy" and the Wasserstein gradient flow of the relative entropy functional, a metric version of Brenier's Theorem, and a new (stronger) definition of Ricci curvature bound from below for metric measure spaces. This new notion is stable w.r.t. measured Gromov-Hausdorff convergence and it is strictly connected with the linearity of the heat flow.Comment: To the memory of Enrico Magenes, whose exemplar life, research and teaching shaped generations of mathematician

A Two-Step Certified Reduced Basis Method

In this paper we introduce a two-step Certified Reduced Basis (RB) method. In the first step we construct from an expensive finite element “truth” discretization of dimension N an intermediate RB model of dimension N≪N . In the second step we construct from this intermediate RB model a derived RB (DRB) model of dimension M≤N. The construction of the DRB model is effected at cost O(N) and in particular at cost independent of N ; subsequent evaluation of the DRB model may then be effected at cost O(M) . The DRB model comprises both the DRB output and a rigorous a posteriori error bound for the error in the DRB output with respect to the truth discretization. The new approach is of particular interest in two contexts: focus calculations and hp-RB approximations. In the former the new approach serves to reduce online cost, M≪N: the DRB model is restricted to a slice or subregion of a larger parameter domain associated with the intermediate RB model. In the latter the new approach enlarges the class of problems amenable to hp-RB treatment by a significant reduction in offline (precomputation) cost: in the development of the hp parameter domain partition and associated “local” (now derived) RB models the finite element truth is replaced by the intermediate RB model. We present numerical results to illustrate the new approach.United States. Air Force Office of Scientific Research (AFOSR Grant number FA9550-07-1-0425)United States. Department of Defense. Office of the Secretary of Defense (OSD/AFOSR Grant number FA9550-09-1-0613)Norwegian University of Science and Technolog

Comparison of some Reduced Representation Approximations

In the field of numerical approximation, specialists considering highly complex problems have recently proposed various ways to simplify their underlying problems. In this field, depending on the problem they were tackling and the community that are at work, different approaches have been developed with some success and have even gained some maturity, the applications can now be applied to information analysis or for numerical simulation of PDE's. At this point, a crossed analysis and effort for understanding the similarities and the differences between these approaches that found their starting points in different backgrounds is of interest. It is the purpose of this paper to contribute to this effort by comparing some constructive reduced representations of complex functions. We present here in full details the Adaptive Cross Approximation (ACA) and the Empirical Interpolation Method (EIM) together with other approaches that enter in the same category