{"title":"Hybrid high-order methods for flow simulations in extremely large discrete fracture networks","authors":"A. Ern, Florent Hédin, G. Pichot, Nicolas Pignet","doi":"10.5802/smai-jcm.92","DOIUrl":"https://doi.org/10.5802/smai-jcm.92","url":null,"abstract":"","PeriodicalId":376888,"journal":{"name":"The SMAI journal of computational mathematics","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114476521","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}
. We propose and study a family of formally second-order accurate schemes to approximate weak solutions of hyperbolic systems of conservation laws. Theses schemes are based on a dissipative property satisfied by the second-order discretization in space. They are proven to satisfy a global entropy inequality for a generic strictly convex entropy. These schemes do not involve limitation techniques. Numerical results are provided to illustrate their accuracy and stability.
{"title":"A family of second-order dissipative finite volume schemes for hyperbolic systems of conservation laws","authors":"M. Badsi, C. Berthon, Ludovic Martaud","doi":"10.5802/smai-jcm.94","DOIUrl":"https://doi.org/10.5802/smai-jcm.94","url":null,"abstract":". We propose and study a family of formally second-order accurate schemes to approximate weak solutions of hyperbolic systems of conservation laws. Theses schemes are based on a dissipative property satisfied by the second-order discretization in space. They are proven to satisfy a global entropy inequality for a generic strictly convex entropy. These schemes do not involve limitation techniques. Numerical results are provided to illustrate their accuracy and stability.","PeriodicalId":376888,"journal":{"name":"The SMAI journal of computational mathematics","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127980819","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}
G. Pichot, Simon Legrand, M. Kern, Nathanael Tepakbong-Tematio
. The Circulant Embedding Method (CEM) is a well known technique to generate stationary Gaussian Random Fields (GRF). The main idea is to embed the covariance matrix in a larger nested block circulant matrix, whose factorization can be rapidly computed thanks to the fast Fourier transform (FFT) algorithm. The CEM requires the extended matrix to be at least positive semidefinite which is proven to be the case if the enclosing domain is sufficiently large, as proven by Theorem 2.3 in [9] for cubic domains. In this paper, we generalize this theorem to the case of rectangular parallelepipeds. Then we propose a new initialization stage of the CEM algorithm that makes it possible to quickly jump to a domain size close to the one needed for the CEM algorithm to work. These domain size estimates are based on fitting functions. Examples of fitting functions are given for the Matérn family of covariances. These functions are inspired by our numerical simulations and by the theoretical work from [9]. The parameters estimation of the fitting functions is done numerically. Several numerical tests are performed to show the efficiency of the proposed algorithms, for both isotropic and anisotropic Matérn covariances.
{"title":"Initialization of the Circulant Embedding method to speed up the generation of Gaussian random fields","authors":"G. Pichot, Simon Legrand, M. Kern, Nathanael Tepakbong-Tematio","doi":"10.5802/smai-jcm.89","DOIUrl":"https://doi.org/10.5802/smai-jcm.89","url":null,"abstract":". The Circulant Embedding Method (CEM) is a well known technique to generate stationary Gaussian Random Fields (GRF). The main idea is to embed the covariance matrix in a larger nested block circulant matrix, whose factorization can be rapidly computed thanks to the fast Fourier transform (FFT) algorithm. The CEM requires the extended matrix to be at least positive semidefinite which is proven to be the case if the enclosing domain is sufficiently large, as proven by Theorem 2.3 in [9] for cubic domains. In this paper, we generalize this theorem to the case of rectangular parallelepipeds. Then we propose a new initialization stage of the CEM algorithm that makes it possible to quickly jump to a domain size close to the one needed for the CEM algorithm to work. These domain size estimates are based on fitting functions. Examples of fitting functions are given for the Matérn family of covariances. These functions are inspired by our numerical simulations and by the theoretical work from [9]. The parameters estimation of the fitting functions is done numerically. Several numerical tests are performed to show the efficiency of the proposed algorithms, for both isotropic and anisotropic Matérn covariances.","PeriodicalId":376888,"journal":{"name":"The SMAI journal of computational mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128928358","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}
M. Boileau, Bérenger Bramas, E. Franck, Romane Hélie, P. Helluy, L. Navoret
. We present an efficient solver for the conservative transport equation with variable coefficients in complex toroidal geometries. The solver is based on a kinetic formulation resembling the Lattice-Boltzmann approach. The chosen formalism allows obtaining an explicit and conservative scheme that requires no matrix inversion and whose CFL stability condition is independent from the poloidal dynamics. We present the method and its optimized parallel implementation on toroidal geometries. Two and three dimensional plasma physics test cases are carried out.
{"title":"Parallel kinetic scheme for transport equations in complex toroidal geometry","authors":"M. Boileau, Bérenger Bramas, E. Franck, Romane Hélie, P. Helluy, L. Navoret","doi":"10.5802/smai-jcm.86","DOIUrl":"https://doi.org/10.5802/smai-jcm.86","url":null,"abstract":". We present an efficient solver for the conservative transport equation with variable coefficients in complex toroidal geometries. The solver is based on a kinetic formulation resembling the Lattice-Boltzmann approach. The chosen formalism allows obtaining an explicit and conservative scheme that requires no matrix inversion and whose CFL stability condition is independent from the poloidal dynamics. We present the method and its optimized parallel implementation on toroidal geometries. Two and three dimensional plasma physics test cases are carried out.","PeriodicalId":376888,"journal":{"name":"The SMAI journal of computational mathematics","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116838982","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}
Given $n$ samples of a function $fcolon Dtomathbb C$ in random points drawn with respect to a measure $varrho_S$ we develop theoretical analysis of the $L_2(D, varrho_T)$-approximation error. For a parituclar choice of $varrho_S$ depending on $varrho_T$, it is known that the weighted least squares method from finite dimensional function spaces $V_m$, $dim(V_m) = m
给定$n$关于测量$varrho_S$的函数$fcolon Dtomathbb C$随机点的样本，我们对$L_2(D, varrho_T)$ -近似误差进行了理论分析。对于依赖于$varrho_T$的$varrho_S$的特定选择，众所周知，有限维函数空间$V_m$, $dim(V_m) = m
{"title":"Error Guarantees for Least Squares Approximation with Noisy Samples in Domain Adaptation","authors":"Felix Bartel","doi":"10.5802/smai-jcm.96","DOIUrl":"https://doi.org/10.5802/smai-jcm.96","url":null,"abstract":"Given $n$ samples of a function $fcolon Dtomathbb C$ in random points drawn with respect to a measure $varrho_S$ we develop theoretical analysis of the $L_2(D, varrho_T)$-approximation error. For a parituclar choice of $varrho_S$ depending on $varrho_T$, it is known that the weighted least squares method from finite dimensional function spaces $V_m$, $dim(V_m) = m<infty$ has the same error as the best approximation in $V_m$ up to a multiplicative constant when given exact samples with logarithmic oversampling. If the source measure $varrho_S$ and the target measure $varrho_T$ differ we are in the domain adaptation setting, a subfield of transfer learning. We model the resulting deterioration of the error in our bounds. Further, for noisy samples, our bounds describe the bias-variance trade off depending on the dimension $m$ of the approximation space $V_m$. All results hold with high probability. For demonstration, we consider functions defined on the $d$-dimensional cube given in unifom random samples. We analyze polynomials, the half-period cosine, and a bounded orthonormal basis of the non-periodic Sobolev space $H_{mathrm{mix}}^2$. Overcoming numerical issues of this $H_{text{mix}}^2$ basis, this gives a novel stable approximation method with quadratic error decay. Numerical experiments indicate the applicability of our results.","PeriodicalId":376888,"journal":{"name":"The SMAI journal of computational mathematics","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126397414","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}
. In this paper, we investigate the effect of the space and time discretisation on the convergence properties of Schwarz Waveform Relaxation (SWR) algorithms. We consider a reaction-diffusion problem with discontinuous coefficients discretised on two non-overlapping domains with several numerical schemes (in space and time). A methodology to determine the rate of convergence of the classical SWR method with standard interface conditions (Dirichlet-Neumann or Robin-Robin) accounting for discretisation errors is presented. We discuss how such convergence rates differ from the ones derived at a continuous level (i.e. assuming an exact discrete representation of the continuous problem). In this work we consider a second-order finite difference scheme and a finite volume scheme based on quadratic spline reconstruction in space, combined with either a simple backward Euler scheme or a two-step “Padé” scheme (resembling a Diagonally Implicit Runge Kutta scheme) in time. We prove those combinations of space-time schemes to be unconditionally stable on bounded domains. We illustrate the relevance of our analysis with specifically designed numerical experiments.
{"title":"Discrete analysis of Schwarz waveform relaxation for a diffusion reaction problem with discontinuous coefficients","authors":"Simon Clément, F. Lemarié, E. Blayo","doi":"10.5802/smai-jcm.81","DOIUrl":"https://doi.org/10.5802/smai-jcm.81","url":null,"abstract":". In this paper, we investigate the effect of the space and time discretisation on the convergence properties of Schwarz Waveform Relaxation (SWR) algorithms. We consider a reaction-diffusion problem with discontinuous coefficients discretised on two non-overlapping domains with several numerical schemes (in space and time). A methodology to determine the rate of convergence of the classical SWR method with standard interface conditions (Dirichlet-Neumann or Robin-Robin) accounting for discretisation errors is presented. We discuss how such convergence rates differ from the ones derived at a continuous level (i.e. assuming an exact discrete representation of the continuous problem). In this work we consider a second-order finite difference scheme and a finite volume scheme based on quadratic spline reconstruction in space, combined with either a simple backward Euler scheme or a two-step “Padé” scheme (resembling a Diagonally Implicit Runge Kutta scheme) in time. We prove those combinations of space-time schemes to be unconditionally stable on bounded domains. We illustrate the relevance of our analysis with specifically designed numerical experiments.","PeriodicalId":376888,"journal":{"name":"The SMAI journal of computational mathematics","volume":"644 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121607385","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}
. Boundary element methods are a well-established technique for solving linear boundary value problems for electrostatic potentials. In this context we present a novel way to approximate the forces exerted by electrostatic fields on conducting objects. Like the standard post-processing technique employing surface integrals derived from the Maxwell stress tensor the new approach solely relies on surface integrals, but, compared to the former, offers better accuracy and faster convergence. The new formulas arise from the interpretation of forces fields as shape derivatives, in the spirit of the virtual work principle, combined with the adjoint approach from shape optimization. In contrast to standard formulas, they meet the continuity and smoothing requirements of abstract duality arguments, which supply a rigorous underpinning for their observed superior performance. 2020 Mathematics Subject Classification. 65N38, 78M15, 45A05. Abstract. Boundary element methods are a well-established technique for solving bound- ary value problems for electrostatic potentials. In this context we present a novel way to ap- proximate the forces exerted by fi elds on conducting objects. Like the standard post-processing technique employing surface integrals derived from the Maxwell stress tensor the new approach solely relies on surface integrals, but, compared to the former, o ff ers better accuracy and faster convergence. The new formulas arise from the interpretation of forces fi elds as shape derivatives, in the spirit of the virtual work principle, combined with the adjoint from shape optimiza-
{"title":"Electrostatic Force Computation with Boundary Element Methods","authors":"P. Panchal, R. Hiptmair","doi":"10.5802/smai-jcm.79","DOIUrl":"https://doi.org/10.5802/smai-jcm.79","url":null,"abstract":". Boundary element methods are a well-established technique for solving linear boundary value problems for electrostatic potentials. In this context we present a novel way to approximate the forces exerted by electrostatic fields on conducting objects. Like the standard post-processing technique employing surface integrals derived from the Maxwell stress tensor the new approach solely relies on surface integrals, but, compared to the former, offers better accuracy and faster convergence. The new formulas arise from the interpretation of forces fields as shape derivatives, in the spirit of the virtual work principle, combined with the adjoint approach from shape optimization. In contrast to standard formulas, they meet the continuity and smoothing requirements of abstract duality arguments, which supply a rigorous underpinning for their observed superior performance. 2020 Mathematics Subject Classification. 65N38, 78M15, 45A05. Abstract. Boundary element methods are a well-established technique for solving bound- ary value problems for electrostatic potentials. In this context we present a novel way to ap- proximate the forces exerted by fi elds on conducting objects. Like the standard post-processing technique employing surface integrals derived from the Maxwell stress tensor the new approach solely relies on surface integrals, but, compared to the former, o ff ers better accuracy and faster convergence. The new formulas arise from the interpretation of forces fi elds as shape derivatives, in the spirit of the virtual work principle, combined with the adjoint from shape optimiza-","PeriodicalId":376888,"journal":{"name":"The SMAI journal of computational mathematics","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130004389","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. Bernard, A. Cohen, Arnaud Guyader Lpsm, Cermics, F. Malrieu
Let g : $Omega$ = [0, 1] d $rightarrow$ R denote a Lipschitz function that can be evaluated at each point, but at the price of a heavy computational time. Let X stand for a random variable with values in $Omega$ such that one is able to simulate, at least approximately, according to the restriction of the law of X to any subset of $Omega$. For example, thanks to Markov chain Monte Carlo techniques, this is always possible when X admits a density that is known up to a normalizing constant. In this context, given a deterministic threshold T such that the failure probability p := P(g(X)>T) may be very low, our goal is to estimate the latter with a minimal number of calls to g. In this aim, building on Cohen et al. [9], we propose a recursive and optimal algorithm that selects on the fly areas of interest and estimate their respective probabilities.
设g: $Omega$ = [0,1] d $rightarrow$ R表示可以在每个点求值的Lipschitz函数，但代价是大量的计算时间。设X代表一个随机变量，其值为$Omega$，使得人们能够根据X定律的限制，至少近似地模拟$Omega$的任何子集。例如，由于马尔可夫链蒙特卡罗技术，当X承认一个已知的密度直到一个归一化常数时，这总是可能的。在这种情况下，给定一个确定性阈值T，使得失效概率p:= p (g(X)>T)可能非常低，我们的目标是通过对g的最小调用次数来估计后者。为此，在Cohen等人[9]的基础上，我们提出了一种递归的最优算法，该算法在飞行中选择感兴趣的区域并估计其各自的概率。
{"title":"Recursive Estimation of a Failure Probability for a Lipschitz Function","authors":"L. Bernard, A. Cohen, Arnaud Guyader Lpsm, Cermics, F. Malrieu","doi":"10.5802/smai-jcm.80","DOIUrl":"https://doi.org/10.5802/smai-jcm.80","url":null,"abstract":"Let g : $Omega$ = [0, 1] d $rightarrow$ R denote a Lipschitz function that can be evaluated at each point, but at the price of a heavy computational time. Let X stand for a random variable with values in $Omega$ such that one is able to simulate, at least approximately, according to the restriction of the law of X to any subset of $Omega$. For example, thanks to Markov chain Monte Carlo techniques, this is always possible when X admits a density that is known up to a normalizing constant. In this context, given a deterministic threshold T such that the failure probability p := P(g(X)>T) may be very low, our goal is to estimate the latter with a minimal number of calls to g. In this aim, building on Cohen et al. [9], we propose a recursive and optimal algorithm that selects on the fly areas of interest and estimate their respective probabilities.","PeriodicalId":376888,"journal":{"name":"The SMAI journal of computational mathematics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132645001","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}
. We numerically study the planar evolution by curvature flow of three parametrised curves that are connected by a triple junction in which conditions are imposed on the angles at which the curves meet. One of the key problems in analysing motion of networks by curvature law is the choice of a tangential velocity that allows for motion of the triple junction, does not lead to mesh degeneration, and is amenable to an error analysis. Our approach consists in considering a perturbation of a classical smooth formulation. The problem we propose admits a natural variational formulation that can be discretized with finite elements. The perturbation can be made arbitrarily small when a regularisation parameter shrinks to zero. Convergence of the new semi-discrete finite element scheme including optimal error estimates are proved. These results are supported by some numerical tests. Finally, the influence of the small regularisation parameter on the properties of scheme and the accuracy of the results is numerically investigated.
{"title":"On motion by curvature of a network with a triple junction","authors":"Paola Pozzi, B. Stinner","doi":"10.5802/SMAI-JCM.70","DOIUrl":"https://doi.org/10.5802/SMAI-JCM.70","url":null,"abstract":". We numerically study the planar evolution by curvature flow of three parametrised curves that are connected by a triple junction in which conditions are imposed on the angles at which the curves meet. One of the key problems in analysing motion of networks by curvature law is the choice of a tangential velocity that allows for motion of the triple junction, does not lead to mesh degeneration, and is amenable to an error analysis. Our approach consists in considering a perturbation of a classical smooth formulation. The problem we propose admits a natural variational formulation that can be discretized with finite elements. The perturbation can be made arbitrarily small when a regularisation parameter shrinks to zero. Convergence of the new semi-discrete finite element scheme including optimal error estimates are proved. These results are supported by some numerical tests. Finally, the influence of the small regularisation parameter on the properties of scheme and the accuracy of the results is numerically investigated.","PeriodicalId":376888,"journal":{"name":"The SMAI journal of computational mathematics","volume":"136 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115476982","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}
In this work, the POD-DEIM-based parareal method introduced in [6] is implemented for the resolution of the two-dimensional nonlinear shallow water equations using a finite volume scheme. This method is a variant of the traditional parareal method, first introduced by [19], that improves the stability and convergence for nonlinear hyperbolic problems, and uses reduced-order models constructed via the Proper Orthogonal Decomposition-Discrete Empirical Interpolation Method (POD-DEIM) applied to snapshots of the solution of the parareal iterations. We propose a modification of this parareal method for further stability and convergence improvements. It consists in enriching the snapshots set for the POD-DEIM procedure with extra snapshots whose computation does not require any additional computational cost. The performances of the classical parareal method, the POD-DEIM-based parareal method and our proposed modification are compared using numerical tests with increasing complexity. Our modified method shows a more stable behaviour and converges in fewer iterations than the other two methods.
{"title":"Modified parareal method for solving the two-dimensional nonlinear shallow water equations using finite volumes","authors":"J. G. C. Steinstraesser, V. Guinot, A. Rousseau","doi":"10.5802/smai-jcm.75","DOIUrl":"https://doi.org/10.5802/smai-jcm.75","url":null,"abstract":"In this work, the POD-DEIM-based parareal method introduced in [6] is implemented for the resolution of the two-dimensional nonlinear shallow water equations using a finite volume scheme. This method is a variant of the traditional parareal method, first introduced by [19], that improves the stability and convergence for nonlinear hyperbolic problems, and uses reduced-order models constructed via the Proper Orthogonal Decomposition-Discrete Empirical Interpolation Method (POD-DEIM) applied to snapshots of the solution of the parareal iterations. We propose a modification of this parareal method for further stability and convergence improvements. It consists in enriching the snapshots set for the POD-DEIM procedure with extra snapshots whose computation does not require any additional computational cost. The performances of the classical parareal method, the POD-DEIM-based parareal method and our proposed modification are compared using numerical tests with increasing complexity. Our modified method shows a more stable behaviour and converges in fewer iterations than the other two methods.","PeriodicalId":376888,"journal":{"name":"The SMAI journal of computational mathematics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131000195","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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