GAMM Mitteilungen最新文献

{"title":"A literature survey of matrix methods for data science","authors":"Martin Stoll","doi":"10.1002/gamm.202000013","DOIUrl":"10.1002/gamm.202000013","url":null,"abstract":"<p>Efficient numerical linear algebra is a core ingredient in many applications across almost all scientific and industrial disciplines. With this survey we want to illustrate that numerical linear algebra has played and is playing a crucial role in enabling and improving data science computations with many new developments being fueled by the availability of data and computing resources. We highlight the role of various different factorizations and the power of changing the representation of the data as well as discussing topics such as randomized algorithms, functions of matrices, and high-dimensional problems. We briefly touch upon the role of techniques from numerical linear algebra used within deep learning.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"43 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202000013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72476180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Topical Issue Applied and Numerical Linear Algebra (1/2)","authors":"Stefan Güttel,&nbsp;Jörg Liesen","doi":"10.1002/gamm.202000020","DOIUrl":"10.1002/gamm.202000020","url":null,"abstract":"","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"43 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81851177","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":"Matrix functions in network analysis","authors":"Michele Benzi,&nbsp;Paola Boito","doi":"10.1002/gamm.202000012","DOIUrl":"10.1002/gamm.202000012","url":null,"abstract":"<p>We review the recent use of functions of matrices in the analysis of graphs and networks, with special focus on centrality and communicability measures and diffusion processes. Both undirected and directed networks are considered, as well as dynamic (temporal) networks. Computational issues are also addressed.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"43 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79600590","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":"Numerical linear algebra in data assimilation","authors":"Melina A. Freitag","doi":"10.1002/gamm.202000014","DOIUrl":"10.1002/gamm.202000014","url":null,"abstract":"<p>Data assimilation is a method that combines observations (ie, real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output. The model is usually represented by a discretized partial differential equation. The data assimilation problem can be formulated as a large scale Bayesian inverse problem. Based on this interpretation we will derive the most important variational and sequential data assimilation approaches, in particular three-dimensional and four-dimensional variational data assimilation (3D-Var and 4D-Var) and the Kalman filter. We will then consider more advanced methods which are extensions of the Kalman filter and variational data assimilation and pay particular attention to their advantages and disadvantages. The data assimilation problem usually results in a very large optimization problem and/or a very large linear system to solve (due to inclusion of time and space dimensions). Therefore, the second part of this article aims to review advances and challenges, in particular from the numerical linear algebra perspective, within the various data assimilation approaches.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"43 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.202000014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85018547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling and simulation of human induced pluripotent stem cell-derived cardiac tissue","authors":"Alexander Jung,&nbsp;Manfred Staat","doi":"10.1002/gamm.202000011","DOIUrl":"10.1002/gamm.202000011","url":null,"abstract":"<p> </p><p>In the discussion section of Jung and Staat<span>¹</span>, the statement “a factor of 1000 when the ventricular-like” should be corrected to “a factor of 10 if the ventricular-like”.</p><p>The online version has been corrected.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"43 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202000011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90943111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A mixed least-squares finite element formulation with explicit consideration of the balance of moment of momentum, a numerical study","authors":"Maximilian Igelbüscher,&nbsp;Jörg Schröder,&nbsp;Alexander Schwarz","doi":"10.1002/gamm.202000009","DOIUrl":"10.1002/gamm.202000009","url":null,"abstract":"<p>Important conditions in structural analysis are the fulfillment of the balance of linear momentum (vanishing resultant forces) and the balance of angular momentum (vanishing resultant moment), which is not a priori satisfied for arbitrary element formulations. In this contribution, we analyze a mixed least-squares (LS) finite element formulation for linear elasticity with explicit consideration of the balance of angular momentum. The considered stress-displacement (<span><b>σ</b></span> − <span><b><i>u</i></b></span>) formulation is based on the squared <span><i>L</i>²(ℬ)</span>-norm minimization of the residuals of a first-order system of differential equations. The formulation is constructed by means of two residuals, that is, the balance of linear momentum and the constitutive equation. Motivated by the crucial point of weighting factors within LS formulations, a scale independent formulation is constructed. The displacement approximation is performed by standard Lagrange polynomials and the stress approximation with Raviart-Thomas functions. The latter ansatz functions do not a priori fulfill the symmetry of the Cauchy stress tensor. Therefore, a redundant residual, the balance of angular momentum (<span>(<b><i>x</i></b> − <b><i>x</i></b>₀) × (div<b>σ</b> + <b><i>f</i></b>) + axl[<b>σ</b> − <b>σ</b>^<i>T</i>]</span>), is introduced and the results are discussed from the engineering point of view, especially for coarse mesh discretizations. However, this formulation shows an improvement compared to standard LS <span><b>σ</b> − <b><i>u</i></b></span> formulations, which is considered here in a numerical study.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"43 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202000009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86912386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Preface GAMM Mitteilungen","authors":"Jörg Schröder,&nbsp;Thomas Wick","doi":"10.1002/gamm.202000010","DOIUrl":"10.1002/gamm.202000010","url":null,"abstract":"The aim of this Priority Programme is to pool expertise of mathematics and mechanics in Germany and to create new collaborations and strengthen existing networks. Over the last years the main objective of the Priority Programme has been the development of modern nonconventional discretization's, based on for example, mixed (Galerkin or least-squares) finite elements, discontinuous Galerkin formulations, finite cell methods, collocation techniques, or isogeometric analysis. These developments include the mathematical analysis for geometrically as well as physically nonlinear problems in the fields of, for instance, incompressibility, anisotropies, and discontinuities (cracks or contact). Numerical simulation techniques are an essential component for the construction, design and optimization of cutting-edge technologies as for example innovative products, new materials as well as medical-technical applications and production processes. These important developments pose great demands on the quality, reliability, and efficiency of numerical methods, which are used for the simulation of the aforementioned complex problems. Existing computer-based solution methods often provide approximations, which cannot guarantee or fulfill substantial, absolutely necessary stability criteria. Specifically in the field of geometrical and material nonlinearities such uncertainties appear. Consequently, the Priority Programme 1748 focuses on novel approaches for reliable simulation techniques in solid mechanics, especially in the development of nonstandard discretization methods accompanied with mechanical and mathematical analysis. The topics addressed in this special issue will deal with mathematical and mechanical aspects of nonconventional discretization methods. The investigation of the sensitivity of phase-field approaches with respect to model specific parameters, that is, the critical length of regularization, the degradation function and the mobility is discussed in “A detailed investigation of the model influencing parameters of the phase-field fracture approach” by C. Bilgen, A. Kopaničáková, R. Krause, and K. Weinberg. The insights of diffusive models for fracture formulations are presented by a phase field model for ductile fracture with linear isotropic hardening in “3D phase field simulations of ductile fracture” by T. Noll, C. Kuhn, D. Olesch, and R. Müller. A stress equilibration procedure for hyperelastic material models based on a displacement-pressure approximation is investigated in the paper “Weakly symmetric stress equilibrium for hyperelastic material models” by F. Bertrand, M. Moldenhauer, and G. Starke. A mixed least-squares formulation with explicit consideration of the balance of angular momentum is discussed from an engineering point of view for the fulfillment of support reactions in the contribution “A mixed least-squares finite element formulation with explicit consideration of the balance of moment of momentum, a numerical study” by M.","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"43 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202000010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77998616","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":"Preface GAMM Mitteilungen","authors":"Jörg Schröder,&nbsp;Thomas Wick","doi":"10.1002/gamm.202000006","DOIUrl":"10.1002/gamm.202000006","url":null,"abstract":"The aim of this Priority Programme is to pool the expertise of mathematics and mechanics in Germany and to create new collaborations and strengthen existing networks. Over the last years, the main objective of the Priority Programme has been the development of modern, nonconventional discretizations based on, for example, mixed (Galerkin or least-squares) finite elements, discontinuous Galerkin formulations, finite cell methods, collocation techniques, or isogeometric analysis. These developments include the mathematical analysis for geometrically, as well as physically, nonlinear problems in the fields of, for instance, incompressibility, anisotropies, and discontinuities (cracks or contact). Numerical simulation techniques are an essential component for the construction, design, and optimization of cutting-edge technologies as, for example, innovative products, new materials and medical-technical applications, and production processes. These important developments pose great demands on the quality, reliability, and efficiency of numerical methods, which are used for the simulation of the aforementioned complex problems. Existing computer-based solution methods often provide approximations, which cannot guarantee or fulfill substantial, absolutely necessary stability criteria. Such uncertainties appear specifically in the field of geometrical and material nonlinearities. Consequently, the Priority Programme 1748 focuses on novel approaches for reliable simulation techniques in solid mechanics, especially in the development of nonstandard discretization methods accompanied by mechanical and mathematical analysis. The topics addressed in this special issue will deal with mathematical and mechanical aspects of nonconventional discretization methods. An application of a diffuse modeling approach for embedded material interfaces to nonconforming meshes is presented for linear elasticity in the paper “A diffuse modeling approach for embedded interfaces in linear elasticity” by P. Hennig, R. Maier, D. Peterseim, D. Schillinger, B. Verfürth, and M. Kästner. Mixed finite-element formulations for gradient elasticity are presented in a finite strain hyperelastic setting in the contribution “Three-field mixed finite element formulations for gradient elasticity at finite strains” by the authors J. Riesselmann, J. Ketteler, M. Schedensack, and D. Balzani. The investigation of mesh adaptivity for monolithic phase-field fractures in brittle materials by a reliable and efficient residual-type error estimator is discussed in the contribution “Mesh adaptivity for quasi-static phase-field fractures based on a residual-type a posteriori error estimator” by K. Mang, M. Walloth, T. Wick, and W. Wollner. The application of hp-basis functions with higher differentiability properties in the context of the finite cell method and numerical simulations on complex geometries is presented in “hp-basis functions of higher differentiability in the Finite Cell Method” by S. Koll","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202000006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73988405","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":"3D phase field simulations of ductile fracture","authors":"Timo Noll,&nbsp;Charlotte Kuhn,&nbsp;Darius Olesch,&nbsp;Ralf Müller","doi":"10.1002/gamm.202000008","DOIUrl":"10.1002/gamm.202000008","url":null,"abstract":"<p>In this contribution a phase field model for ductile fracture with linear isotropic hardening is presented. An energy functional consisting of an elastic energy, a plastic dissipation potential and a Griffith type fracture energy constitutes the model. The application of an unaltered radial return algorithm on element level is possible due to the choice of an appropriate coupling between the nodal degrees of freedom, namely the displacement and the crack/fracture fields. The degradation function models the mentioned coupling by reducing the stiffness of the material and the plastic contribution of the energy density in broken material. Furthermore, to solve the global system of differential equations comprising the balance of linear momentum and the quasi-static Ginzburg-Landau type evolution equation, the application of a monolithic iterative solution scheme becomes feasible. The compact model is used to perform 3D simulations of fracture in tension. The computed plastic zones are compared to the dog-bone model that is used to derive validity criteria for <i>K</i>_IC measurements.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"43 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202000008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86259319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weakly symmetric stress equilibration for hyperelastic material models","authors":"Fleurianne Bertrand,&nbsp;Marcel Moldenhauer,&nbsp;Gerhard Starke","doi":"10.1002/gamm.202000007","DOIUrl":"10.1002/gamm.202000007","url":null,"abstract":"<p>A stress equilibration procedure for hyperelastic material models is proposed and analyzed in this paper. Based on the displacement-pressure approximation computed with a stable finite element pair, it constructs, in a vertex-patch-wise manner, an <i>H</i>(div)-conforming approximation to the first Piola-Kirchhoff stress. This is done in such a way that its associated Cauchy stress is weakly symmetric in the sense that its antisymmetric part is zero tested against continuous piecewise linear functions. Our main result is the identification of the subspace of test functions perpendicular to the range of the local equilibration system on each patch which turn out to be rigid body modes associated with the current configuration. Momentum balance properties are investigated analytically and numerically and the resulting stress reconstruction is shown to provide improved results for surface traction forces by computational experiments.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"43 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202000007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80651709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}