Special Issue "Computational Methods for Coupled Problems in Science and Engineering"

A special issue of Mathematical and Computational Applications (ISSN 2297-8747).

Deadline for manuscript submissions: closed (15 January 2022) | Viewed by 13415

Special Issue Editors

Prof. Dr. Simona Perotto
E-Mail Website
Guest Editor
MOX—Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
Interests: approximation of partial differential equations; isotropic and anisotropic mesh generation and adaptation; a priori and a posteriori error estimators; model reduction techniques; adaptive reduced order modeling; computational fluid dynamics; blood flow modeling; topology optimization; design of metamaterials; crack detection; aerospace applications; image segmentation; optimized rendering of 3D graphical objects
Prof. Dr. Gianluigi Rozza
E-Mail Website
Guest Editor
SISSA mathLab, International School for Advanced Studies, Office A-435, Via Bonomea 265, 34136 Trieste, Italy
Interests: numerical analysis and scientific computing; reduced order modelling and methods; efficient reduced-basis methods for parametrized PDEs and a posteriori error estimation; computational fluid dynamics: aero-naval-mechanical engineering; blood flows (haemodynamics); environmental fluid dynamics; multi-physics; software in computational science and engineering
Special Issues, Collections and Topics in MDPI journals
Dr. Antonia Larese
E-Mail Website
Guest Editor
Department of Mathematics, Università degli Studi di Padova, via Trieste 1, 35121 Padova, Italy
Interests: computational mechanics; computational fluid dynamics (CFD); fluid structure interaction (FSI); coupled problems; particle methods; embedded/immersed techniques for FSI; non-Newtonian materials

Special Issue Information

Dear Colleagues,

This Special Issue will collect contributions from the IX International Conference on Computational Methods for Coupled Problems in Science and Engineering (https://coupled2021.cimne.com/). Papers considered to fit the scope of the journal and to be of exceptional quality, after evaluation by the reviewers, will be published free of charge.

Prof. Dr. Simona Perotto
Prof. Dr. Gianluigi Rozza
Dr. Antonia Larese
Guest Editors

Manuscript Submission Information

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Published Papers (9 papers)

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Research

Article
Enhancing Quasi-Newton Acceleration for Fluid-Structure Interaction
Math. Comput. Appl. 2022, 27(3), 40; https://doi.org/10.3390/mca27030040 - 06 May 2022
Cited by 1 | Viewed by 1100
Abstract
We propose two enhancements of quasi-Newton methods used to accelerate coupling iterations for partitioned fluid-structure interaction. Quasi-Newton methods have been established as flexible, yet robust, efficient and accurate coupling methods of multi-physics simulations in general. The coupling library preCICE provides several variants, the [...] Read more.
We propose two enhancements of quasi-Newton methods used to accelerate coupling iterations for partitioned fluid-structure interaction. Quasi-Newton methods have been established as flexible, yet robust, efficient and accurate coupling methods of multi-physics simulations in general. The coupling library preCICE provides several variants, the so-called IQN-ILS method being the most commonly used. It uses input and output differences of the coupled solvers collected in previous iterations and time steps to approximate Newton iterations. To make quasi-Newton methods both applicable for parallel coupling (where these differences contain data from different physical fields) and to provide a robust approach for re-using information, a combination of information filtering and scaling for the different physical fields is typically required. This leads to good convergence, but increases the cost per iteration. We propose two new approaches—pre-scaling weight monitoring and a new, so-called QR3 filter, to substantially improve runtime while not affecting convergence quality. We evaluate these for a variety of fluid-structure interaction examples. Results show that we achieve drastic speedups for the pure quasi-Newton update steps. In the future, we intend to apply the methods also to volume-coupled scenarios, where these gains can be decisive for the feasibility of the coupling approach. Full article
(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)
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Article
A Trust Region Reduced Basis Pascoletti-Serafini Algorithm for Multi-Objective PDE-Constrained Parameter Optimization
Math. Comput. Appl. 2022, 27(3), 39; https://doi.org/10.3390/mca27030039 - 03 May 2022
Cited by 1 | Viewed by 943
Abstract
In the present paper non-convex multi-objective parameter optimization problems are considered which are governed by elliptic parametrized partial differential equations (PDEs). To solve these problems numerically the Pascoletti-Serafini scalarization is applied and the obtained scalar optimization problems are solved by an augmented Lagrangian [...] Read more.
In the present paper non-convex multi-objective parameter optimization problems are considered which are governed by elliptic parametrized partial differential equations (PDEs). To solve these problems numerically the Pascoletti-Serafini scalarization is applied and the obtained scalar optimization problems are solved by an augmented Lagrangian method. However, due to the PDE constraints, the numerical solution is very expensive so that a model reduction is utilized by using the reduced basis (RB) method. The quality of the RB approximation is ensured by a trust-region strategy which does not require any offline procedure, in which the RB functions are computed in a greedy algorithm. Moreover, convergence of the proposed method is guaranteed and different techniques to prevent the excessive growth of the number of basis functions are explored. Numerical examples illustrate the efficiency of the proposed solution technique. Full article
(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)
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Article
Challenges in Kinetic-Kinematic Driven Musculoskeletal Subject-Specific Infant Modeling
Math. Comput. Appl. 2022, 27(3), 36; https://doi.org/10.3390/mca27030036 - 22 Apr 2022
Viewed by 1241
Abstract
Musculoskeletal computational models provide a non-invasive approach to investigate human movement biomechanics. These models could be particularly useful for pediatric applications where in vivo and in vitro biomechanical parameters are difficult or impossible to examine using physical experiments alone. The objective was to [...] Read more.
Musculoskeletal computational models provide a non-invasive approach to investigate human movement biomechanics. These models could be particularly useful for pediatric applications where in vivo and in vitro biomechanical parameters are difficult or impossible to examine using physical experiments alone. The objective was to develop a novel musculoskeletal subject-specific infant model to investigate hip joint biomechanics during cyclic leg movements. Experimental motion-capture marker data of a supine-lying 2-month-old infant were placed on a generic GAIT 2392 OpenSim model. After scaling the model using body segment anthropometric measurements and joint center locations, inverse kinematics and dynamics were used to estimate hip ranges of motion and moments. For the left hip, a maximum moment of 0.975 Nm and a minimum joint moment of 0.031 Nm were estimated at 34.6° and 65.5° of flexion, respectively. For the right hip, a maximum moment of 0.906 Nm and a minimum joint moment of 0.265 Nm were estimated at 23.4° and 66.5° of flexion, respectively. Results showed agreement with reported values from the literature. Further model refinements and validations are needed to develop and establish a normative infant dataset, which will be particularly important when investigating the movement of infants with pathologies such as developmental dysplasia of the hip. This research represents the first step in the longitudinal development of a model that will critically contribute to our understanding of infant growth and development during the first year of life. Full article
(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)
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Article
Reduced Order Modeling Using Advection-Aware Autoencoders
Math. Comput. Appl. 2022, 27(3), 34; https://doi.org/10.3390/mca27030034 - 21 Apr 2022
Cited by 2 | Viewed by 1595
Abstract
Physical systems governed by advection-dominated partial differential equations (PDEs) are found in applications ranging from engineering design to weather forecasting. They are known to pose severe challenges to both projection-based and non-intrusive reduced order modeling, especially when linear subspace approximations are used. In [...] Read more.
Physical systems governed by advection-dominated partial differential equations (PDEs) are found in applications ranging from engineering design to weather forecasting. They are known to pose severe challenges to both projection-based and non-intrusive reduced order modeling, especially when linear subspace approximations are used. In this work, we develop an advection-aware (AA) autoencoder network that can address some of these limitations by learning efficient, physics-informed, nonlinear embeddings of the high-fidelity system snapshots. A fully non-intrusive reduced order model is developed by mapping the high-fidelity snapshots to a latent space defined by an AA autoencoder, followed by learning the latent space dynamics using a long-short-term memory (LSTM) network. This framework is also extended to parametric problems by explicitly incorporating parameter information into both the high-fidelity snapshots and the encoded latent space. Numerical results obtained with parametric linear and nonlinear advection problems indicate that the proposed framework can reproduce the dominant flow features even for unseen parameter values. Full article
(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)
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Article
Coupled Neural–Glial Dynamics and the Role of Astrocytes in Alzheimer’s Disease
Math. Comput. Appl. 2022, 27(3), 33; https://doi.org/10.3390/mca27030033 - 21 Apr 2022
Cited by 1 | Viewed by 1287
Abstract
Neurodegenerative diseases such as Alzheimer’s (AD) are associated with the propagation and aggregation of toxic proteins. In the case of AD, it was Alzheimer himself who showed the importance of both amyloid beta (Aβ) plaques and tau protein neurofibrillary tangles [...] Read more.
Neurodegenerative diseases such as Alzheimer’s (AD) are associated with the propagation and aggregation of toxic proteins. In the case of AD, it was Alzheimer himself who showed the importance of both amyloid beta (Aβ) plaques and tau protein neurofibrillary tangles (NFTs) in what he called the “disease of forgetfulness”. The amyloid beta forms extracellular aggregates and plaques, whereas tau proteins are intracellular proteins that stabilize axons by cross-linking microtubules that can form largely messy tangles. On the other hand, astrocytes and microglial cells constantly clear these plaques and NFTs from the brain. Astrocytes transport nutrients from the blood to neurons. Activated astrocytes produce monocyte chemoattractant protein-1 (MCP-1), which attracts anti-inflammatory macrophages and clears Aβ. At the same time, the microglia cells are poorly phagocytic for Aβ compared to proinflammatory and anti-inflammatory macrophages. In addition to such distinctive neuropathological features of AD as amyloid beta and tau proteins, neuroinflammation has to be brought into the picture as well. Taking advantage of a coupled mathematical modelling framework, we formulate a network model, accounting for the coupling between neurons and astroglia and integrating all three main neuropathological features with the brain connectome data. We provide details on the coupled dynamics involving cytokines, astrocytes, and microglia. Further, we apply the tumour necrosis factor alpha (TNF-α) inhibitor and anti-Aβ drug and analyze their influence on the brain cells, suggesting conditions under which the drug can prevent cell damage. The important role of astrocytes and TNF-α inhibitors in AD pathophysiology is emphasized, along with potentially promising pathways for developing new AD therapies. Full article
(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)
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Article
Benchmarking Regridding Libraries Used in Earth System Modelling
Math. Comput. Appl. 2022, 27(2), 31; https://doi.org/10.3390/mca27020031 - 01 Apr 2022
Cited by 1 | Viewed by 1418
Abstract
Components of Earth system models (ESMs) usually use different numerical grids because of the different environments they represent. Therefore, a coupling field sent by a source model has to be regridded to be used by a target model. The regridding has to be [...] Read more.
Components of Earth system models (ESMs) usually use different numerical grids because of the different environments they represent. Therefore, a coupling field sent by a source model has to be regridded to be used by a target model. The regridding has to be accurate and, in some cases, conservative, in order to ensure the consistency of the coupled model. Here, we present work done to benchmark the quality of four regridding libraries currently used in ESMs, i.e., SCRIP, YAC, ESMF and XIOS. We evaluated five regridding algorithms with four different analytical functions for different combinations of six grids used in real ocean or atmosphere models. Four analytical functions were used to define the coupling fields to be regridded. This benchmark calculated some of the metrics proposed by the CANGA project, including the mean, maximum, RMS misfit, and global conservation. The results show that, besides a few very specific cases that present anomalous values, the regridding functionality in YAC, ESMF and XIOS can be considered of high quality and do not present the specific problems observed for the conservative SCRIP remapping. The evaluation of the computing performance of those libraries is not included in the current work but is planned to be performed in the coming months. This exercise shows that benchmarking can be a great opportunity to favour interactions between users and developers of regridding libraries. Full article
(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)
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Article
Multi-Physics Inverse Homogenization for the Design of Innovative Cellular Materials: Application to Thermo-Elastic Problems
Math. Comput. Appl. 2022, 27(1), 15; https://doi.org/10.3390/mca27010015 - 15 Feb 2022
Cited by 1 | Viewed by 1466
Abstract
We present a new algorithm to design lightweight cellular materials with required properties in a multi-physics context. In particular, we focus on a thermo-elastic setting by promoting the design of unit cells characterized both by an isotropic and an anisotropic behavior with respect [...] Read more.
We present a new algorithm to design lightweight cellular materials with required properties in a multi-physics context. In particular, we focus on a thermo-elastic setting by promoting the design of unit cells characterized both by an isotropic and an anisotropic behavior with respect to mechanical and thermal requirements. The proposed procedure generalizes the microSIMPATY algorithm to a thermo-elastic framework by preserving all the good properties of the reference design methodology. The resulting layouts exhibit non-standard topologies and are characterized by very sharp contours, thus limiting the post-processing before manufacturing. The new cellular materials are compared with the state-of-art in engineering practice in terms of thermo-elastic properties, thus highlighting the good performance of the new layouts which, in some cases, outperform the consolidated choices. Full article
(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)
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Article
Modified Representations for the Close Evaluation Problem
Math. Comput. Appl. 2021, 26(4), 69; https://doi.org/10.3390/mca26040069 - 28 Sep 2021
Viewed by 1498
Abstract
When using boundary integral equation methods, we represent solutions of a linear partial differential equation as layer potentials. It is well-known that the approximation of layer potentials using quadrature rules suffer from poor resolution when evaluated closed to (but not on) the boundary. [...] Read more.
When using boundary integral equation methods, we represent solutions of a linear partial differential equation as layer potentials. It is well-known that the approximation of layer potentials using quadrature rules suffer from poor resolution when evaluated closed to (but not on) the boundary. To address this challenge, we provide modified representations of the problem’s solution. Similar to Gauss’s law used to modify Laplace’s double-layer potential, we use modified representations of Laplace’s single-layer potential and Helmholtz layer potentials that avoid the close evaluation problem. Some techniques have been developed in the context of the representation formula or using interpolation techniques. We provide alternative modified representations of the layer potentials directly (or when only one density is at stake). Several numerical examples illustrate the efficiency of the technique in two and three dimensions. Full article
(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)
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Article
Towards Building the OP-Mapped WENO Schemes: A General Methodology
by and
Math. Comput. Appl. 2021, 26(4), 67; https://doi.org/10.3390/mca26040067 - 23 Sep 2021
Cited by 5 | Viewed by 1474
Abstract
A serious and ubiquitous issue in existing mapped WENO schemes is that most of them can hardly preserve high resolutions, but in the meantime prevent spurious oscillations in the solving of hyperbolic conservation laws with long output times. Our goal for this article [...] Read more.
A serious and ubiquitous issue in existing mapped WENO schemes is that most of them can hardly preserve high resolutions, but in the meantime prevent spurious oscillations in the solving of hyperbolic conservation laws with long output times. Our goal for this article was to address this widely known problem. In our previous work, the order-preserving (OP) criterion was originally introduced and carefully used to devise a new mapped WENO scheme that performs satisfactorily in long simulations, and hence it was indicated that the OP criterion plays a critical role in the maintenance of low-dissipation and robustness for mapped WENO schemes. Thus, in our present work, we firstly defined the family of mapped WENO schemes, whose mappings meet the OP criterion, as OP-Mapped WENO. Next, we attentively took a closer look at the mappings of various existing mapped WENO schemes and devised a general formula for them. That helped us to extend the OP criterion to the design of improved mappings. Then, we created a generalized implementation of obtaining a group of OP-Mapped WENO schemes, named MOP-WENO-X, as they are developed from the existing mapped WENO-X schemes, where the notation “X” is used to identify the version of the existing mapped WENO scheme. Finally, extensive numerical experiments and comparisons with competing schemes were conducted to demonstrate the enhanced performances of the MOP-WENO-X schemes. Full article
(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)
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