In this paper, we study the generalized multiscale finite element method (GMsFEM) for single phase compressible flow in highly heterogeneous porous media. We follow the major steps of the GMsFEM to construct permeability dependent offline basis for fast coarse-grid simulation. The offline coarse space is efficiently constructed only once based on the initial permeability field with parallel computing. A rigorous convergence analysis is performed for two types of snapshot spaces. The analysis indicates that the convergence rates of the proposed multiscale method depend on the coarse meshsize and the eigenvalue decay of the local spectral problem. To further increase the accuracy of multiscale method, residual driven online multiscale basis is added to the offline space. The construction of online multiscale basis is based on a carefully design error indicator motivated by the analysis. We find that online basis is particularly important for the singular source. Rich numerical tests on typical 3D highly heterogeneous medias are presented to demonstrate the impressive computational advantages of the proposed multiscale method.
{"title":"Generalized multiscale finite element method for highly heterogeneous compressible flow","authors":"Shubin Fu, Eric T. Chung, Lina Zhao","doi":"10.1137/21m1438475","DOIUrl":"https://doi.org/10.1137/21m1438475","url":null,"abstract":"In this paper, we study the generalized multiscale finite element method (GMsFEM) for single phase compressible flow in highly heterogeneous porous media. We follow the major steps of the GMsFEM to construct permeability dependent offline basis for fast coarse-grid simulation. The offline coarse space is efficiently constructed only once based on the initial permeability field with parallel computing. A rigorous convergence analysis is performed for two types of snapshot spaces. The analysis indicates that the convergence rates of the proposed multiscale method depend on the coarse meshsize and the eigenvalue decay of the local spectral problem. To further increase the accuracy of multiscale method, residual driven online multiscale basis is added to the offline space. The construction of online multiscale basis is based on a carefully design error indicator motivated by the analysis. We find that online basis is particularly important for the singular source. Rich numerical tests on typical 3D highly heterogeneous medias are presented to demonstrate the impressive computational advantages of the proposed multiscale method.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125308787","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}
When waves propagate through a complex medium like the turbulent atmosphere the wave field becomes incoherent and the wave intensity forms a complex speckle pattern. In this paper we study a speckle memory effect in the frequency domain and some of its consequences. This effect means that certain properties of the speckle pattern produced by wave transmission through a randomly scattering medium is preserved when shifting the frequency of the illumination. The speckle memory effect is characterized via a detailed novel analysis of the fourth-order moment of the random paraxial Green's function at four different frequencies. We arrive at a precise characterization of the frequency memory effect and what governs the strength of the memory. As an application we quantify the statistical stability of time-reversal wave refocusing through a randomly scattering medium in the paraxial or beam regime. Time reversal refers to the situation when a transmitted wave field is recorded on a time-reversal mirror then time reversed and sent back into the complex medium. The reemitted wave field then refocuses at the original source point. We compute the mean of the refocused wave and identify a novel quantitative description of its variance in terms of the radius of the time-reversal mirror, the size of its elements, the source bandwidth and the statistics of the random medium fluctuations.
{"title":"Speckle Memory Effect in the Frequency Domain and Stability in Time-Reversal Experiments","authors":"J. Garnier, K. Sølna","doi":"10.1137/22m1470414","DOIUrl":"https://doi.org/10.1137/22m1470414","url":null,"abstract":"When waves propagate through a complex medium like the turbulent atmosphere the wave field becomes incoherent and the wave intensity forms a complex speckle pattern. In this paper we study a speckle memory effect in the frequency domain and some of its consequences. This effect means that certain properties of the speckle pattern produced by wave transmission through a randomly scattering medium is preserved when shifting the frequency of the illumination. The speckle memory effect is characterized via a detailed novel analysis of the fourth-order moment of the random paraxial Green's function at four different frequencies. We arrive at a precise characterization of the frequency memory effect and what governs the strength of the memory. As an application we quantify the statistical stability of time-reversal wave refocusing through a randomly scattering medium in the paraxial or beam regime. Time reversal refers to the situation when a transmitted wave field is recorded on a time-reversal mirror then time reversed and sent back into the complex medium. The reemitted wave field then refocuses at the original source point. We compute the mean of the refocused wave and identify a novel quantitative description of its variance in terms of the radius of the time-reversal mirror, the size of its elements, the source bandwidth and the statistics of the random medium fluctuations.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125512418","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 article we develop the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for elliptic partial differential equations with inhomogeneous Dirichlet, Neumann, and Robin boundary conditions, and the high contrast property emerges from the coefficients of elliptic operators and Robin boundary conditions. By careful construction of multiscale bases of the CEM-GMsFEM, we introduce two operators $mathcal{D}^m$ and $mathcal{N}^m$ which are used to handle inhomogeneous Dirichlet and Neumann boundary values and are also proved to converge independently of contrast ratios as enlarging oversampling regions. We provide a priori error estimate and show that oversampling layers are the key factor in controlling numerical errors. A series of experiments are conducted, and those results reflect the reliability of our methods even with high contrast ratios.
{"title":"Constraint energy minimizing generalized multiscale finite element method for inhomogeneous boundary value problems with high contrast coefficients","authors":"Changqing Ye, Eric T. Chung","doi":"10.1137/21m1459113","DOIUrl":"https://doi.org/10.1137/21m1459113","url":null,"abstract":"In this article we develop the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for elliptic partial differential equations with inhomogeneous Dirichlet, Neumann, and Robin boundary conditions, and the high contrast property emerges from the coefficients of elliptic operators and Robin boundary conditions. By careful construction of multiscale bases of the CEM-GMsFEM, we introduce two operators $mathcal{D}^m$ and $mathcal{N}^m$ which are used to handle inhomogeneous Dirichlet and Neumann boundary values and are also proved to converge independently of contrast ratios as enlarging oversampling regions. We provide a priori error estimate and show that oversampling layers are the key factor in controlling numerical errors. A series of experiments are conducted, and those results reflect the reliability of our methods even with high contrast ratios.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"149 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122458741","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 establish improved uniform error bounds on time-splitting methods for the long-time dynamics of the Dirac equation with small electromagnetic potentials characterized by a dimensionless parameter $varepsilonin (0, 1]$ representing the amplitude of the potentials. We begin with a semi-discritization of the Dirac equation in time by a time-splitting method, and then followed by a full-discretization in space by the Fourier pseudospectral method. Employing the unitary flow property of the second-order time-splitting method for the Dirac equation, we prove uniform error bounds at $C(t)tau^2$ and $C(t)(h^m+tau^2)$ for the semi-discretization and full-discretization, respectively, for any time $tin[0,T_varepsilon]$ with $T_varepsilon = T/varepsilon$ for $T>0$, which are uniformly for $varepsilon in (0, 1]$, where $tau$ is the time step, $h$ is the mesh size, $mgeq 2$ depends on the regularity of the solution, and $C(t) = C_0 + C_1varepsilon tle C_0+C_1T$ grows at most linearly with respect to $t$ with $C_0ge0$ and $C_1>0$ two constants independent of $t$, $h$, $tau$ and $varepsilon$. Then by adopting the regularity compensation oscillation (RCO) technique which controls the high frequency modes by the regularity of the solution and low frequency modes by phase cancellation and energy method, we establish improved uniform error bounds at $O(varepsilontau^2)$ and $O(h^m +varepsilontau^2)$ for the semi-discretization and full-discretization, respectively, up to the long-time $T_varepsilon$. Numerical results are reported to confirm our error bounds and to demonstrate that they are sharp. Comparisons on the accuracy of different time discretizations for the Dirac equation are also provided.
{"title":"Improved uniform error bounds on time-splitting methods for the long-time dynamics of the Dirac equation with small potentials","authors":"W. Bao, Yue Feng, Jia Yin","doi":"10.1137/22m146995x","DOIUrl":"https://doi.org/10.1137/22m146995x","url":null,"abstract":"We establish improved uniform error bounds on time-splitting methods for the long-time dynamics of the Dirac equation with small electromagnetic potentials characterized by a dimensionless parameter $varepsilonin (0, 1]$ representing the amplitude of the potentials. We begin with a semi-discritization of the Dirac equation in time by a time-splitting method, and then followed by a full-discretization in space by the Fourier pseudospectral method. Employing the unitary flow property of the second-order time-splitting method for the Dirac equation, we prove uniform error bounds at $C(t)tau^2$ and $C(t)(h^m+tau^2)$ for the semi-discretization and full-discretization, respectively, for any time $tin[0,T_varepsilon]$ with $T_varepsilon = T/varepsilon$ for $T>0$, which are uniformly for $varepsilon in (0, 1]$, where $tau$ is the time step, $h$ is the mesh size, $mgeq 2$ depends on the regularity of the solution, and $C(t) = C_0 + C_1varepsilon tle C_0+C_1T$ grows at most linearly with respect to $t$ with $C_0ge0$ and $C_1>0$ two constants independent of $t$, $h$, $tau$ and $varepsilon$. Then by adopting the regularity compensation oscillation (RCO) technique which controls the high frequency modes by the regularity of the solution and low frequency modes by phase cancellation and energy method, we establish improved uniform error bounds at $O(varepsilontau^2)$ and $O(h^m +varepsilontau^2)$ for the semi-discretization and full-discretization, respectively, up to the long-time $T_varepsilon$. Numerical results are reported to confirm our error bounds and to demonstrate that they are sharp. Comparisons on the accuracy of different time discretizations for the Dirac equation are also provided.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"4564 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122196346","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, a two-scale approach for elastic shape optimization of fine-scale structures in additive manufacturing is investigated. To this end, a free material optimization is performed on the macro-scale using elasticity tensors in a set of microscopically realizable tensors. A database of these realizable tensors and their cost values is obtained with a shape and topology optimization on microscopic cells, working within a fixed set of elasticity tensors samples. This microscopic optimization takes into account manufacturability constraints via predefined material bridges to neighbouring cells at the faces of the microscopic fundamental cell. For the actual additive manufacturing on a chosen fine-scale, a piece-wise constant elasticity tensor ansatz on grid cells of a macroscopic mesh is applied. The macroscopic optimization is performed in an efficient online phase, whereas the associated cell-wise optimal material patterns are retrieved from the database that was computed offline. For that, the set of admissible realizable elasticity tensors is parametrized using tensor product cubic B-splines over the unit square matching the precomputed samples. This representation is then efficiently used in an interior point method for the free material optimization on the macro-scale.
{"title":"Two-scale elastic shape optimization for additive manufacturing","authors":"S. Conti, M. Rumpf, Stefan Simon","doi":"10.1137/21m1450859","DOIUrl":"https://doi.org/10.1137/21m1450859","url":null,"abstract":"In this paper, a two-scale approach for elastic shape optimization of fine-scale structures in additive manufacturing is investigated. To this end, a free material optimization is performed on the macro-scale using elasticity tensors in a set of microscopically realizable tensors. A database of these realizable tensors and their cost values is obtained with a shape and topology optimization on microscopic cells, working within a fixed set of elasticity tensors samples. This microscopic optimization takes into account manufacturability constraints via predefined material bridges to neighbouring cells at the faces of the microscopic fundamental cell. For the actual additive manufacturing on a chosen fine-scale, a piece-wise constant elasticity tensor ansatz on grid cells of a macroscopic mesh is applied. The macroscopic optimization is performed in an efficient online phase, whereas the associated cell-wise optimal material patterns are retrieved from the database that was computed offline. For that, the set of admissible realizable elasticity tensors is parametrized using tensor product cubic B-splines over the unit square matching the precomputed samples. This representation is then efficiently used in an interior point method for the free material optimization on the macro-scale.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"36 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120969465","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}
Triadic closure describes the tendency for new friendships to form between individuals who already have friends in common. It has been argued heuristically that the triadic closure effect can lead to bistability in the formation of large-scale social interaction networks. Here, depending on the initial state and the transient dynamics, the system may evolve towards either of two long-time states. In this work, we propose and study a hierarchy of network evolution models that incorporate triadic closure, building on the work of Grindrod, Higham, and Parsons [Internet Mathematics, 8, 2012, 402--423]. We use a chemical kinetics framework, paying careful attention to the reaction rate scaling with respect to the system size. In a macroscale regime, we show rigorously that a bimodal steady-state distribution is admitted. This behavior corresponds to the existence of two distinct stable fixed points in a deterministic mean-field ODE. The macroscale model is also seen to capture an apparent metastability property of the microscale system. Computational simulations are used to support the analysis.
{"title":"A Hierarchy of Network Models Giving Bistability Under Triadic Closure","authors":"Stefano Di Giovacchino, D. Higham, K. Zygalakis","doi":"10.1137/21m1461290","DOIUrl":"https://doi.org/10.1137/21m1461290","url":null,"abstract":"Triadic closure describes the tendency for new friendships to form between individuals who already have friends in common. It has been argued heuristically that the triadic closure effect can lead to bistability in the formation of large-scale social interaction networks. Here, depending on the initial state and the transient dynamics, the system may evolve towards either of two long-time states. In this work, we propose and study a hierarchy of network evolution models that incorporate triadic closure, building on the work of Grindrod, Higham, and Parsons [Internet Mathematics, 8, 2012, 402--423]. We use a chemical kinetics framework, paying careful attention to the reaction rate scaling with respect to the system size. In a macroscale regime, we show rigorously that a bimodal steady-state distribution is admitted. This behavior corresponds to the existence of two distinct stable fixed points in a deterministic mean-field ODE. The macroscale model is also seen to capture an apparent metastability property of the microscale system. Computational simulations are used to support the analysis.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126155503","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}
S. Ephrati, Erwin Luesink, G. Wimmer, P. Cifani, B. Geurts
Small-scale features of shallow water flow obtained from direct numerical simulation (DNS) with two different computational codes for the shallow water equations are gathered offline and subsequently employed with the aim of constructing a reduced-order correction. This is used to facilitate high-fidelity online flow predictions at much reduced costs on coarse meshes. The resolved small-scale features at high resolution represent subgrid properties for the coarse representation. Measurements of the subgrid dynamics are obtained as the difference between the evolution of a coarse grid solution and the corresponding DNS result. The measurements are sensitive to the particular numerical methods used for the simulation on coarse computational grids and can be used to approximately correct the associated discretization errors. The subgrid features are decomposed into empirical orthogonal functions (EOFs), after which a corresponding correction term is constructed. By increasing the number of EOFs in the approximation of the measured values the correction term can in principle be made arbitrarily accurate. Both computational methods investigated here show a significant decrease in the simulation error already when applying the correction based on the dominant EOFs only. The error reduction accounts for the particular discretization errors that incur and are hence specific to the particular simulation method that is adopted. This improvement is also observed for very coarse grids which may be used for computational model reduction in geophysical and turbulent flow problems.
{"title":"Computational Modeling for High-Fidelity Coarsening of Shallow Water Equations Based on Subgrid Data","authors":"S. Ephrati, Erwin Luesink, G. Wimmer, P. Cifani, B. Geurts","doi":"10.1137/21m1452871","DOIUrl":"https://doi.org/10.1137/21m1452871","url":null,"abstract":"Small-scale features of shallow water flow obtained from direct numerical simulation (DNS) with two different computational codes for the shallow water equations are gathered offline and subsequently employed with the aim of constructing a reduced-order correction. This is used to facilitate high-fidelity online flow predictions at much reduced costs on coarse meshes. The resolved small-scale features at high resolution represent subgrid properties for the coarse representation. Measurements of the subgrid dynamics are obtained as the difference between the evolution of a coarse grid solution and the corresponding DNS result. The measurements are sensitive to the particular numerical methods used for the simulation on coarse computational grids and can be used to approximately correct the associated discretization errors. The subgrid features are decomposed into empirical orthogonal functions (EOFs), after which a corresponding correction term is constructed. By increasing the number of EOFs in the approximation of the measured values the correction term can in principle be made arbitrarily accurate. Both computational methods investigated here show a significant decrease in the simulation error already when applying the correction based on the dominant EOFs only. The error reduction accounts for the particular discretization errors that incur and are hence specific to the particular simulation method that is adopted. This improvement is also observed for very coarse grids which may be used for computational model reduction in geophysical and turbulent flow problems.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129254939","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 consider a particle undergoing diffusion with stochastic resetting in a bounded domain $calUsubset R^d$ for $d=2,3$. The domain is perforated by a set of partially absorbing targets within which the particle may be absorbed at a rate $kappa$. Each target is assumed to be much smaller than $|calU|$, which allows us to use asymptotic and Green's function methods to solve the diffusion equation in Laplace space. In particular, we construct an inner solution within the interior and local exterior of each target, and match it with an outer solution in the bulk of $calU$. This yields an asymptotic expansion of the Laplace transformed flux into each target in powers of $nu=-1/ln epsilon$ ($d=2$) and $epsilon$ ($d=3$), respectively, where $epsilon$ is the non-dimensionalized target size. The fluxes determine how the mean first-passage time to absorption depends on the reaction rate $kappa$ and the resetting rate $r$. For a range of parameter values, the MFPT is a unimodal function of $r$, with a minimum at an optimal resetting rate $r_{rm opt}$ that depends on $kappa$ and the target configuration.
{"title":"The Narrow Capture Problem with Partially Absorbing Targets and Stochastic Resetting","authors":"P. Bressloff, Ryan D. Schumm","doi":"10.1137/21m1449580","DOIUrl":"https://doi.org/10.1137/21m1449580","url":null,"abstract":"We consider a particle undergoing diffusion with stochastic resetting in a bounded domain $calUsubset R^d$ for $d=2,3$. The domain is perforated by a set of partially absorbing targets within which the particle may be absorbed at a rate $kappa$. Each target is assumed to be much smaller than $|calU|$, which allows us to use asymptotic and Green's function methods to solve the diffusion equation in Laplace space. In particular, we construct an inner solution within the interior and local exterior of each target, and match it with an outer solution in the bulk of $calU$. This yields an asymptotic expansion of the Laplace transformed flux into each target in powers of $nu=-1/ln epsilon$ ($d=2$) and $epsilon$ ($d=3$), respectively, where $epsilon$ is the non-dimensionalized target size. The fluxes determine how the mean first-passage time to absorption depends on the reaction rate $kappa$ and the resetting rate $r$. For a range of parameter values, the MFPT is a unimodal function of $r$, with a minimum at an optimal resetting rate $r_{rm opt}$ that depends on $kappa$ and the target configuration.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127425186","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, we apply the finite element heterogeneous multiscale method to a class of dispersive first-order time-dependent Maxwell systems. For this purpose, we use an analytic homogenization result, which shows that the effective system contains additional dispersive effects. We provide a careful study of the (time-dependent) micro problems, including $H^2$ and micro errors estimates. Eventually, we prove a semi-discrete error estimate for the method.
{"title":"The Heterogeneous Multiscale Method for dispersive Maxwell systems","authors":"P. Freese","doi":"10.1137/21M1443960","DOIUrl":"https://doi.org/10.1137/21M1443960","url":null,"abstract":"In this work, we apply the finite element heterogeneous multiscale method to a class of dispersive first-order time-dependent Maxwell systems. For this purpose, we use an analytic homogenization result, which shows that the effective system contains additional dispersive effects. We provide a careful study of the (time-dependent) micro problems, including $H^2$ and micro errors estimates. Eventually, we prove a semi-discrete error estimate for the method.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116763828","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 prove the possibility of achieving non-reciprocal wave propagation in space-time modulated media and give an asymptotic analysis of the non-reciprocity property in terms of the amplitude of the time-modulation. Such modulation causes a folding of the band structure of the material, which may induce degenerate points. By breaking time-reversal symmetry, we show that these degeneracies may open into non-symmetric, unidirectional band gaps. Finally we illustrate our results by several numerical simulations.
{"title":"NonReciprocal Wave Propagation in Space-Time Modulated Media","authors":"H. Ammari, Jinghao Cao, Erik Orvehed Hiltunen","doi":"10.1137/21m1449427","DOIUrl":"https://doi.org/10.1137/21m1449427","url":null,"abstract":"We prove the possibility of achieving non-reciprocal wave propagation in space-time modulated media and give an asymptotic analysis of the non-reciprocity property in terms of the amplitude of the time-modulation. Such modulation causes a folding of the band structure of the material, which may induce degenerate points. By breaking time-reversal symmetry, we show that these degeneracies may open into non-symmetric, unidirectional band gaps. Finally we illustrate our results by several numerical simulations.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130881831","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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