Pub Date : 2026-01-09DOI: 10.1016/j.cma.2025.118666
Faisal As’ad, Charbel Farhat
We introduce a computationally tractable framework for multiscale homogenization of path-dependent heterogeneous materials that combines mechanics-informed artificial neural networks with a staggered training procedure. The proposed approach decomposes complex, multiscale problems into a sequence of two-scale subproblems, efficiently bridging the scales through data-driven, neural network-based surrogate models that are, by construction, consistent with fundamental laws of continuum mechanics. The staggered training strategy ensures that the offline computational cost scales linearly with the number of scales, rather than exponentially, thereby achieving substantial efficiency gains over conventional nested multiscale finite element methods. As an illustrative application, the framework is demonstrated on woven fabrics, capturing viscoelastic and fiber-resolved material behaviors while maintaining computational efficiency. The results demonstrate that the proposed method achieves high-fidelity predictions comparable to those of fully resolved models reconstructed from real-material imaging, establishing a general and flexible methodology for modeling complex materials with many interacting scales.
{"title":"A staggered training framework for mechanics-informed neural networks in tractable multiscale homogenization with application to woven fabrics","authors":"Faisal As’ad, Charbel Farhat","doi":"10.1016/j.cma.2025.118666","DOIUrl":"10.1016/j.cma.2025.118666","url":null,"abstract":"<div><div>We introduce a computationally tractable framework for multiscale homogenization of path-dependent heterogeneous materials that combines mechanics-informed artificial neural networks with a staggered training procedure. The proposed approach decomposes complex, multiscale problems into a sequence of two-scale subproblems, efficiently bridging the scales through data-driven, neural network-based surrogate models that are, by construction, consistent with fundamental laws of continuum mechanics. The staggered training strategy ensures that the offline computational cost scales linearly with the number of scales, rather than exponentially, thereby achieving substantial efficiency gains over conventional nested multiscale finite element methods. As an illustrative application, the framework is demonstrated on woven fabrics, capturing viscoelastic and fiber-resolved material behaviors while maintaining computational efficiency. The results demonstrate that the proposed method achieves high-fidelity predictions comparable to those of fully resolved models reconstructed from real-material imaging, establishing a general and flexible methodology for modeling complex materials with many interacting scales.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118666"},"PeriodicalIF":7.3,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-09DOI: 10.1016/j.cma.2025.118721
Maria Roberta Belardo , Francesco Calabrò
Isogeometric collocation discretizes the strong form of a PDE on smooth spline spaces and therefore avoids element integration, but its spatial accuracy is highly sensitive to the placement of the collocation nodes. For this reason methods are tested on linear elliptic problems in order to verify convergence properties. Classical choices such as Greville abscissae may yield suboptimal convergence in both H1 and L2 norms for several spline degrees and problem settings. Node sets derived from (estimated) superconvergent (Cauchy–Galerkin) points – e.g. alternating subsets, clustered variants, or least–squares sets – frequently improve the observed L2 behaviour and in favourable cases approach the Galerkin benchmark, though this is not universal across all degrees, boundary conditions, and PDE types. In this paper we find for the first choices of points that recover optimal convergence for polynomial degrees . The construction is made in order to recover the symmetry inside every knot span also for even degrees, as done in the above mentioned methods. Although the exact reason for this behaviour could not be clearly identified, the numerical evidence suggests that restoring local symmetry recovers the optimal rate. Unfortunately, as most of the previously proposed methods, this results in a collocation system with more equations than degrees of freedom number of degrees of freedom, thus the overall system is solved in a least–square sense.
{"title":"Optimal convergence of IgA collocation methods","authors":"Maria Roberta Belardo , Francesco Calabrò","doi":"10.1016/j.cma.2025.118721","DOIUrl":"10.1016/j.cma.2025.118721","url":null,"abstract":"<div><div>Isogeometric collocation discretizes the strong form of a PDE on smooth spline spaces and therefore avoids element integration, but its spatial accuracy is highly sensitive to the placement of the collocation nodes. For this reason methods are tested on linear elliptic problems in order to verify convergence properties. Classical choices such as Greville abscissae may yield suboptimal convergence in both <em>H</em><sup>1</sup> and <em>L</em><sup>2</sup> norms for several spline degrees and problem settings. Node sets derived from (estimated) superconvergent (Cauchy–Galerkin) points – e.g. alternating subsets, clustered variants, or least–squares sets – frequently improve the observed <em>L</em><sup>2</sup> behaviour and in favourable cases approach the Galerkin benchmark, though this is not universal across all degrees, boundary conditions, and PDE types. In this paper we find for the first choices of points that recover optimal convergence for polynomial degrees <span><math><mrow><mi>p</mi><mo>=</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>8</mn></mrow></math></span>. The construction is made in order to recover the symmetry inside every knot span also for even degrees, as done in the above mentioned methods. Although the exact reason for this behaviour could not be clearly identified, the numerical evidence suggests that restoring local symmetry recovers the optimal rate. Unfortunately, as most of the previously proposed methods, this results in a collocation system with more equations than degrees of freedom number of degrees of freedom, thus the overall system is solved in a least–square sense.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118721"},"PeriodicalIF":7.3,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-08DOI: 10.1016/j.cma.2025.118700
Michał Ł. Mika , René R. Hiemstra , Stein K.F. Stoter , Dominik Schillinger
This paper presents a data-driven approach to develop higher-order accurate tensor-product-stencil quadrature rules for implicitly defined two-dimensional domains. We construct a three-dimensional configuration space of possible domain cuts using a signed distance representation based on circular arcs, defined by their radius and center, and exploit symmetry to simplify its three-dimensional domain. The configuration space, being piecewise smooth, is carefully partitioned into smooth regions, enabling three-dimensional tensor-product spline interpolation to approximate quadrature data sampled from an established implicit domain quadrature technique. The resulting quadrature rules are simple to apply, highly accurate, efficient, and can be used as a black-box solution. We demonstrate compatibility with existing cut finite element techniques and illustrate their application through numerical examples.
{"title":"A data-driven approach to cut-cell quadrature using spline interpolation","authors":"Michał Ł. Mika , René R. Hiemstra , Stein K.F. Stoter , Dominik Schillinger","doi":"10.1016/j.cma.2025.118700","DOIUrl":"10.1016/j.cma.2025.118700","url":null,"abstract":"<div><div>This paper presents a data-driven approach to develop higher-order accurate tensor-product-stencil quadrature rules for implicitly defined two-dimensional domains. We construct a three-dimensional configuration space of possible domain cuts using a signed distance representation based on circular arcs, defined by their radius and center, and exploit symmetry to simplify its three-dimensional domain. The configuration space, being piecewise smooth, is carefully partitioned into smooth regions, enabling three-dimensional tensor-product spline interpolation to approximate quadrature data sampled from an established implicit domain quadrature technique. The resulting quadrature rules are simple to apply, highly accurate, efficient, and can be used as a black-box solution. We demonstrate compatibility with existing cut finite element techniques and illustrate their application through numerical examples.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118700"},"PeriodicalIF":7.3,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-08DOI: 10.1016/j.cma.2025.118664
Christos Papagiannis , Guillaume Balarac , Pietro M. Congedo , Olivier P. Le Maître
In Computational Fluid Dynamics (CFD), and particularly within Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES), the computational cost is largely dictated by the effort required to obtain statistically converged quantities such as time-averaged fields and higher-order moments. Despite the importance of accurately quantifying statistical uncertainty in unsteady simulations, no continuous and cost-effective, on-line method currently exists for monitoring the convergence quality of such statistics during runtime. This work introduces a novel, fully on-line bootstrapping approach to estimate the variance of finite-time averages without requiring the estimation of the flow’s Auto-Correlation Function (ACF). Unlike existing methods that rely on ACF estimation, which are often impractical due to excessive storage demands in large-scale simulations, or require off-line processing or a priori modeling assumptions, our method operates entirely during the simulation and incurs minimal overhead. The proposed technique employs a recursive update of bootstrap replicates of the time average, using correlated random weights generated via an autoregressive model. This formulation is computationally efficient: the update cost scales linearly with the number of bootstrap replicates and the dimensionality of the flow field, and the autoregressive model is inexpensive to evaluate. The method only requires storage of a small number of fields, making it suitable for large-scale CFD applications. We demonstrate the effectiveness of the approach on synthetic data from the Ornstein-Uhlenbeck process and on two canonical LES cases: a turbulent pipe flow and a round jet. We further discuss the method’s applicability to simulations with non-uniform time stepping, highlighting its flexibility and robustness.
{"title":"Autoregressive multiplier bootstrap for in-situ error estimation and quality monitoring of finite time averages in turbulent flow simulations","authors":"Christos Papagiannis , Guillaume Balarac , Pietro M. Congedo , Olivier P. Le Maître","doi":"10.1016/j.cma.2025.118664","DOIUrl":"10.1016/j.cma.2025.118664","url":null,"abstract":"<div><div>In Computational Fluid Dynamics (CFD), and particularly within Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES), the computational cost is largely dictated by the effort required to obtain statistically converged quantities such as time-averaged fields and higher-order moments. Despite the importance of accurately quantifying statistical uncertainty in unsteady simulations, no continuous and cost-effective, on-line method currently exists for monitoring the convergence quality of such statistics during runtime. This work introduces a novel, fully on-line bootstrapping approach to estimate the variance of finite-time averages without requiring the estimation of the flow’s Auto-Correlation Function (ACF). Unlike existing methods that rely on ACF estimation, which are often impractical due to excessive storage demands in large-scale simulations, or require off-line processing or a priori modeling assumptions, our method operates entirely during the simulation and incurs minimal overhead. The proposed technique employs a recursive update of bootstrap replicates of the time average, using correlated random weights generated via an autoregressive model. This formulation is computationally efficient: the update cost scales linearly with the number of bootstrap replicates and the dimensionality of the flow field, and the autoregressive model is inexpensive to evaluate. The method only requires storage of a small number of fields, making it suitable for large-scale CFD applications. We demonstrate the effectiveness of the approach on synthetic data from the Ornstein-Uhlenbeck process and on two canonical LES cases: a turbulent pipe flow and a round jet. We further discuss the method’s applicability to simulations with non-uniform time stepping, highlighting its flexibility and robustness.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118664"},"PeriodicalIF":7.3,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145941000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-08DOI: 10.1016/j.cma.2025.118690
Maximilian Krause , Thomas Böhlke , Matti Schneider
We introduce an efficient computational procedure for generating polycrystalline microstructures which permits studying the influence of specific texture-tensor orders on the resulting effective mechanical response, both in the linear elastic and the inelastic case. The crystallographic texture of a polycrystalline material is described by the Orientation Distribution Function (ODF). For practical computations, only the Fourier coefficients – called texture coefficients – of the ODF up to a certain order are of interest. In the work at hand, we wish to investigate this microstructure-property relationship. We interpret the task of approximating the texture coefficients of a microstructure realization as a moment-matching, i.e., quadrature, problem, and introduce efficient techniques for generating finite sets of orientations which exactly conform to prescribed polynomial texture terms. First, the microstructure morphology is generated via a well-established Laguerre-tessellation-based approach. Subsequently, the crystal grains are assigned a finite set of orientations which realize prescribed texture coefficients. We exploit the sparse representation of the action of the rotation group SO(3) on higher-order tensors to reduce the computational expense from exponential to cubic in the tensor order.
We consider polycrystalline copper as an example material and study the influence of texture terms of different polynomial order on the effective elastic properties and the anisotropy of initial yielding. For a large ensemble of polycrystal microstructures, we find that the elastic properties are mainly influenced by terms up to fourth order, whereas characterizing the yield function accurately requires higher-order texture terms.
To encourage further study of the texture dependence of nonlinear material properties, we provide an open-source python implementation of our algorithm.
{"title":"Generating high-fidelity microstructures of polycrystalline materials with prescribed higher-order texture tensors","authors":"Maximilian Krause , Thomas Böhlke , Matti Schneider","doi":"10.1016/j.cma.2025.118690","DOIUrl":"10.1016/j.cma.2025.118690","url":null,"abstract":"<div><div>We introduce an efficient computational procedure for generating polycrystalline microstructures which permits studying the influence of specific texture-tensor orders on the resulting effective mechanical response, both in the linear elastic and the inelastic case. The crystallographic texture of a polycrystalline material is described by the Orientation Distribution Function (ODF). For practical computations, only the Fourier coefficients – called texture coefficients – of the ODF up to a certain order are of interest. In the work at hand, we wish to investigate this microstructure-property relationship. We interpret the task of approximating the texture coefficients of a microstructure realization as a <em>moment-matching</em>, i.e., quadrature, problem, and introduce efficient techniques for generating finite sets of orientations which exactly conform to prescribed polynomial texture terms. First, the microstructure morphology is generated via a well-established Laguerre-tessellation-based approach. Subsequently, the crystal grains are assigned a finite set of orientations which realize prescribed texture coefficients. We exploit the sparse representation of the action of the rotation group <em>SO</em>(3) on higher-order tensors to reduce the computational expense from exponential to cubic in the tensor order.</div><div>We consider polycrystalline copper as an example material and study the influence of texture terms of different polynomial order on the effective elastic properties and the anisotropy of initial yielding. For a large ensemble of polycrystal microstructures, we find that the elastic properties are mainly influenced by terms up to fourth order, whereas characterizing the yield function accurately requires higher-order texture terms.</div><div>To encourage further study of the texture dependence of nonlinear material properties, we provide an open-source python implementation of our algorithm.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118690"},"PeriodicalIF":7.3,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145941001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-08DOI: 10.1016/j.cma.2025.118701
Stefan Takacs , Stefan Tyoler
Isogeometric Analysis is a variant of the finite element method, where spline functions are used for the representation of both the geometry and the solution. Splines, particularly those with higher degree, achieve their full approximation power only if the solution is sufficiently regular. Since solutions are usually not regular everywhere, adaptive refinement is essential. Recently, a multi-patch-based adaptive refinement strategy based on recursive patch splitting has been proposed, which naturally generates hierarchical, non-matching multi-patch configurations with T-junctions, but preserves the tensor-product structure within each patch. In this work, we investigate the application of the dual-primal Isogeometric Tearing and Interconnecting method (IETI-DP) to such adaptive multi-patch geometries. We provide sufficient conditions for the solvability of the local problems and propose a preconditioner for the overall iterative solver. We establish a condition number bound that coincides with the bound previously shown for the fully matching case. Numerical experiments confirm the theoretical findings and demonstrate the efficiency of the proposed approach in adaptive refinement scenarios.
{"title":"Dual-primal isogeometric tearing and interconnecting solvers for adaptively refined multi-patch configurations","authors":"Stefan Takacs , Stefan Tyoler","doi":"10.1016/j.cma.2025.118701","DOIUrl":"10.1016/j.cma.2025.118701","url":null,"abstract":"<div><div>Isogeometric Analysis is a variant of the finite element method, where spline functions are used for the representation of both the geometry and the solution. Splines, particularly those with higher degree, achieve their full approximation power only if the solution is sufficiently regular. Since solutions are usually not regular everywhere, adaptive refinement is essential. Recently, a multi-patch-based adaptive refinement strategy based on recursive patch splitting has been proposed, which naturally generates hierarchical, non-matching multi-patch configurations with T-junctions, but preserves the tensor-product structure within each patch. In this work, we investigate the application of the dual-primal Isogeometric Tearing and Interconnecting method (IETI-DP) to such adaptive multi-patch geometries. We provide sufficient conditions for the solvability of the local problems and propose a preconditioner for the overall iterative solver. We establish a condition number bound that coincides with the bound previously shown for the fully matching case. Numerical experiments confirm the theoretical findings and demonstrate the efficiency of the proposed approach in adaptive refinement scenarios.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118701"},"PeriodicalIF":7.3,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145941002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-08DOI: 10.1016/j.cma.2025.118681
Stephan Wulfinghoff
The computational homogenization of elastoplastic polycrystals is a challenging task due to the huge number of grains required, their complicated interactions and due to the complexity of crystal plasticity models per se. Despite a few successes of reduced order models, mean field and simplified homogenization approaches often remain the preferred choice. In this work, a recently proposed hyper-reduction method (called E3C) for projection-based Reduced Order Models (pROMs) is applied to the problem of computational homogenization of geometrically linearly deforming elastoplastic polycrystals. The main novelty lies in the identification of reduced modes (the ‘E3C-modes’), which replace the strain modes of the reduced-order model, leading to a significantly smaller number of integration points. The peculiarity, which distinguishes the method from more conventional hyper-reduction techniques, is that the E3C integration points are not taken from the set of FE integration points. Instead, they can be interpreted as generalized integration points in strain space which are trained such as to satisfy an orthogonality condition, which ensures that the hyper-reduced model matches the equilibrium states and macroscopic stresses of full-field model data as accurately as possible. In addition, the number of grains is reduced, preserving the main features of the original texture of the finite element model. Two macroscopic engineering parts (untextured and textured) are simulated, illustrating the performance of the method in three-dimensional two-scale applications involving hundreds of thousands macroscopic degrees of freedom and millions of grains with computing times in the order of hours (cumulated online and offline effort) on standard laptop hardware.
{"title":"Computational crystal plasticity homogenization using empirically corrected cluster cubature (E3C) hyper-reduction","authors":"Stephan Wulfinghoff","doi":"10.1016/j.cma.2025.118681","DOIUrl":"10.1016/j.cma.2025.118681","url":null,"abstract":"<div><div>The computational homogenization of elastoplastic polycrystals is a challenging task due to the huge number of grains required, their complicated interactions and due to the complexity of crystal plasticity models per se. Despite a few successes of reduced order models, mean field and simplified homogenization approaches often remain the preferred choice. In this work, a recently proposed hyper-reduction method (called E3C) for projection-based Reduced Order Models (pROMs) is applied to the problem of computational homogenization of geometrically linearly deforming elastoplastic polycrystals. The main novelty lies in the identification of reduced modes (the ‘E3C-modes’), which replace the strain modes of the reduced-order model, leading to a significantly smaller number of integration points. The peculiarity, which distinguishes the method from more conventional hyper-reduction techniques, is that the E3C integration points are not taken from the set of FE integration points. Instead, they can be interpreted as generalized integration points in strain space which are trained such as to satisfy an orthogonality condition, which ensures that the hyper-reduced model matches the equilibrium states and macroscopic stresses of full-field model data as accurately as possible. In addition, the number of grains is reduced, preserving the main features of the original texture of the finite element model. Two macroscopic engineering parts (untextured and textured) are simulated, illustrating the performance of the method in three-dimensional two-scale applications involving hundreds of thousands macroscopic degrees of freedom and millions of grains with computing times in the order of hours (cumulated online and offline effort) on standard laptop hardware.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118681"},"PeriodicalIF":7.3,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-08DOI: 10.1016/j.cma.2025.118717
Roxan Pulicani , Michael Brun , Olivier Allain , Anthony Gravouil
This paper presents a strongly coupled approach within the Arbitrary Lagrangian-Eulerian (ALE) framework for solving Fluid-Structure Interaction (FSI) problems, such as those involving a deformable structure in a supersonic flow or subjected to a blast loading. The vertex-centered Finite Volume Method (FVM) for the fluid subdomain with two different explicit time integrators (first-order and third-order accurate Runge-Kutta schemes) is coupled with the Finite Element Method (FEM) for the structural subdomain with an implicit time integrator (Newmark Constant Average Acceleration scheme). This coupling is performed using mono- and multi-time step strategies. The proposed FSI algorithms adopts a monolithic and simultaneous FSI coupling, by introducing Lagrange Multipliers (LM) to ensure the continuity of the normal velocity at the Fluid-Structure (FS) interface. This adopted dual Schur approach allows decoupling the FSI problem into two solid and fluid discrete systems, along with an interface discrete system involving the time-dependent Steklov-Poincaré operator and the unknown Lagrange Multipliers. The proposed approach is hybrid (explicit-implicit), strongly coupled, with fluid subcycling, and is non-iterative in the sense that it does not require any subiteration. It provides a compromise between the flexibility of loosely coupled staggered schemes and the robustness of strongly coupled monolithic formulations. The proposed method has been validated for several academic cases and FSI benchmarks, including the classical half shock tube, the one-dimensional piston problem with a rod, the two-dimensional deformable panel subjected to a shock-wave, as well as a two-dimensional panel flutter problem in the supersonic flow regime.
{"title":"A new hybrid strongly coupled multi-time step approach with enhanced robustness for fluid structure interaction problems","authors":"Roxan Pulicani , Michael Brun , Olivier Allain , Anthony Gravouil","doi":"10.1016/j.cma.2025.118717","DOIUrl":"10.1016/j.cma.2025.118717","url":null,"abstract":"<div><div>This paper presents a strongly coupled approach within the Arbitrary Lagrangian-Eulerian (ALE) framework for solving Fluid-Structure Interaction (FSI) problems, such as those involving a deformable structure in a supersonic flow or subjected to a blast loading. The vertex-centered Finite Volume Method (FVM) for the fluid subdomain with two different explicit time integrators (first-order and third-order accurate Runge-Kutta schemes) is coupled with the Finite Element Method (FEM) for the structural subdomain with an implicit time integrator (Newmark Constant Average Acceleration scheme). This coupling is performed using mono- and multi-time step strategies. The proposed FSI algorithms adopts a monolithic and simultaneous FSI coupling, by introducing Lagrange Multipliers (LM) to ensure the continuity of the normal velocity at the Fluid-Structure (FS) interface. This adopted dual Schur approach allows decoupling the FSI problem into two solid and fluid discrete systems, along with an interface discrete system involving the time-dependent Steklov-Poincaré operator and the unknown Lagrange Multipliers. The proposed approach is hybrid (explicit-implicit), strongly coupled, with fluid subcycling, and is non-iterative in the sense that it does not require any subiteration. It provides a compromise between the flexibility of loosely coupled staggered schemes and the robustness of strongly coupled monolithic formulations. The proposed method has been validated for several academic cases and FSI benchmarks, including the classical half shock tube, the one-dimensional piston problem with a rod, the two-dimensional deformable panel subjected to a shock-wave, as well as a two-dimensional panel flutter problem in the supersonic flow regime.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118717"},"PeriodicalIF":7.3,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-08DOI: 10.1016/j.cma.2025.118699
Kamil David Sommer , Lucas Mieg , Siddharth Sharma , Romuald Skoda , Martin Mönnigmann
This research paper investigates the Adjoint Petrov-Galerkin (APG) method for reduced order models (ROMs) and fluid dynamics governed by the semi-discrete incompressible Navier-Stokes equations. The Adjoint Petrov-Galerkin ROM, derived using the Mori-Zwanzig formalism, demonstrates superior accuracy and stability compared to standard Galerkin ROMs. However, challenges arise due to the time invariance of the test basis vectors, resulting in high computational requirements. To address this, we introduce a new efficient Adjoint Petrov-Galerkin (eAPG) ROM formulation, extending its application to the semi-discrete incompressible Navier-Stokes equations. While offline-online decomposition is well established in reduced order modeling, the novelty here lies in its adaptation to the APG framework: by exploiting the polynomial structure of the governing equations, the eAPG formulation eliminates the need for repeated test basis evaluations in the online stage. This reorganization yields an exact offline-online split that improves computational efficiency in comparison to the general APG-ROM formulation. A novel approach to augmenting the memory length, a critical factor influencing the stability and accuracy of the APG-ROM, is introduced, employing a data-driven optimization. Numerical results for the 3D turbulent flow around a circular cylinder demonstrate the efficacy of the proposed approach. Error measures and computational cost evaluations, considering metrics such as floating point operations, memory usage, and simulation time, provide a comprehensive analysis.
{"title":"Efficient Adjoint Petrov-Galerkin reduced order models for fluid flows governed by the semi-discrete incompressible Navier-Stokes equations","authors":"Kamil David Sommer , Lucas Mieg , Siddharth Sharma , Romuald Skoda , Martin Mönnigmann","doi":"10.1016/j.cma.2025.118699","DOIUrl":"10.1016/j.cma.2025.118699","url":null,"abstract":"<div><div>This research paper investigates the Adjoint Petrov-Galerkin (APG) method for reduced order models (ROMs) and fluid dynamics governed by the semi-discrete incompressible Navier-Stokes equations. The Adjoint Petrov-Galerkin ROM, derived using the Mori-Zwanzig formalism, demonstrates superior accuracy and stability compared to standard Galerkin ROMs. However, challenges arise due to the time invariance of the test basis vectors, resulting in high computational requirements. To address this, we introduce a new efficient Adjoint Petrov-Galerkin (eAPG) ROM formulation, extending its application to the semi-discrete incompressible Navier-Stokes equations. While offline-online decomposition is well established in reduced order modeling, the novelty here lies in its adaptation to the APG framework: by exploiting the polynomial structure of the governing equations, the eAPG formulation eliminates the need for repeated test basis evaluations in the online stage. This reorganization yields an exact offline-online split that improves computational efficiency in comparison to the general APG-ROM formulation. A novel approach to augmenting the memory length, a critical factor influencing the stability and accuracy of the APG-ROM, is introduced, employing a data-driven optimization. Numerical results for the 3D turbulent flow around a circular cylinder demonstrate the efficacy of the proposed approach. Error measures and computational cost evaluations, considering metrics such as floating point operations, memory usage, and simulation time, provide a comprehensive analysis.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118699"},"PeriodicalIF":7.3,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-08DOI: 10.1016/j.cma.2025.118709
Sabit Mahmood Khan, Yashar Mehmani
We present a two-level preconditioner for solving linear systems arising from the discretization of the elliptic, linear-elastic deformation equation, in displacement unknowns, over domains with arbitrary geometric and topological complexity and heterogeneity in material properties (including fractures). The preconditioner is an algebraic reformulation of the high-order pore-level multiscale method (hPLMM) proposed recently by the authors, wherein a domain is decomposed into non-overlapping subdomains, and local basis functions are numerically computed over the subdomains to construct a high-quality coarse space (or prolongation matrix). The term “high-order” stands in contrast to the recent low-order PLMM preconditioner, where boundary conditions of local basis problems assume rigidity of all interfaces shared between subdomains. In hPLMM, interfaces are allowed to deform, through the use of suitable mortar spaces, thereby capturing local bending/twisting moments under challenging loading conditions. Benchmarked across a wide range of complex (porous) structures and material heterogeneities, we find hPLMM exhibits superior performance in Krylov solvers than PLMM, as well as state-of-the-art Schwarz and multigrid preconditioners. Applications include risk analysis of subsurface CO2/H2 storage and optimizing porous materials for batteries, prosthetics, and aircraft.
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