Research

16 pages, 3814 KiB

Open AccessArticle

A Computational Fluid Dynamics-Based Model for Assessing Rupture Risk in Cerebral Arteries with Varying Aneurysm Sizes

by Rohan Singla, Shubham Gupta and Arnab Chanda

Math. Comput. Appl. 2023, 28(4), 90; https://doi.org/10.3390/mca28040090 - 02 Aug 2023

Viewed by 1279

A cerebral aneurysm is a medical condition where a cerebral artery can burst under adverse pressure conditions. A 20% mortality rate and additional 30 to 40% morbidity rate have been reported for patients suffering from the rupture of aneurysms. In addition to wall [...] Read more.

A cerebral aneurysm is a medical condition where a cerebral artery can burst under adverse pressure conditions. A 20% mortality rate and additional 30 to 40% morbidity rate have been reported for patients suffering from the rupture of aneurysms. In addition to wall shear stress, input jets, induced pressure, and complicated and unstable flow patterns are other important parameters associated with a clinical history of aneurysm ruptures. In this study, the anterior cerebral artery (ACA) was modeled using image segmentation and then rebuilt with aneurysms at locations vulnerable to aneurysm growth. To simulate various aneurysm growth stages, five aneurysm sizes and two wall thicknesses were taken into consideration. In order to simulate realistic pressure loading conditions for the anterior cerebral arteries, inlet velocity and outlet pressure were used. The pressure, wall shear stress, and flow velocity distributions were then evaluated in order to predict the risk of rupture. A low-wall shear stress-based rupture scenario was created using a smaller aneurysm and thinner walls, which enhanced pressure, shear stress, and flow velocity. Additionally, aneurysms with a 4 mm diameter and a thin wall had increased rupture risks, particularly at specific boundary conditions. It is believed that the findings of this study will help physicians predict rupture risk according to aneurysm diameters and make early treatment decisions. Full article

(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)

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18 pages, 501 KiB

Open AccessFeature PaperArticle

Enhancing Quasi-Newton Acceleration for Fluid-Structure Interaction

by Kyle Davis, Miriam Schulte and Benjamin Uekermann

Math. Comput. Appl. 2022, 27(3), 40; https://doi.org/10.3390/mca27030040 - 06 May 2022

Cited by 4 | Viewed by 1995

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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29 pages, 660 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

A Trust Region Reduced Basis Pascoletti-Serafini Algorithm for Multi-Objective PDE-Constrained Parameter Optimization

by Stefan Banholzer, Luca Mechelli and Stefan Volkwein

Math. Comput. Appl. 2022, 27(3), 39; https://doi.org/10.3390/mca27030039 - 03 May 2022

Cited by 1 | Viewed by 1659

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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11 pages, 3408 KiB

Open AccessArticle

Challenges in Kinetic-Kinematic Driven Musculoskeletal Subject-Specific Infant Modeling

by Yeram Lim, Tamara Chambers, Christine Walck, Safeer Siddicky, Erin Mannen and Victor Huayamave

Math. Comput. Appl. 2022, 27(3), 36; https://doi.org/10.3390/mca27030036 - 22 Apr 2022

Viewed by 2132

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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28 pages, 11190 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Reduced Order Modeling Using Advection-Aware Autoencoders

by Sourav Dutta, Peter Rivera-Casillas, Brent Styles and Matthew W. Farthing

Math. Comput. Appl. 2022, 27(3), 34; https://doi.org/10.3390/mca27030034 - 21 Apr 2022

Cited by 9 | Viewed by 2828

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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14 pages, 1237 KiB

Open AccessArticle

Coupled Neural–Glial Dynamics and the Role of Astrocytes in Alzheimer’s Disease

by Swadesh Pal and Roderick Melnik

Math. Comput. Appl. 2022, 27(3), 33; https://doi.org/10.3390/mca27030033 - 21 Apr 2022

Cited by 2 | Viewed by 2230

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 (

A β

) 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 (

A β

) 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

A β

. At the same time, the microglia cells are poorly phagocytic for

A β

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-

A β

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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26 pages, 11381 KiB

Open AccessFeature PaperArticle

Benchmarking Regridding Libraries Used in Earth System Modelling

by Sophie Valcke, Andrea Piacentini and Gabriel Jonville

Math. Comput. Appl. 2022, 27(2), 31; https://doi.org/10.3390/mca27020031 - 01 Apr 2022

Cited by 4 | Viewed by 2717

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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20 pages, 24807 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Multi-Physics Inverse Homogenization for the Design of Innovative Cellular Materials: Application to Thermo-Elastic Problems

by Matteo Gavazzoni, Nicola Ferro, Simona Perotto and Stefano Foletti

Math. Comput. Appl. 2022, 27(1), 15; https://doi.org/10.3390/mca27010015 - 15 Feb 2022

Cited by 3 | Viewed by 2553

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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21 pages, 3321 KiB

Open AccessArticle

Modified Representations for the Close Evaluation Problem

by Camille Carvalho

Math. Comput. Appl. 2021, 26(4), 69; https://doi.org/10.3390/mca26040069 - 28 Sep 2021

Viewed by 1971

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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46 pages, 13196 KiB

Open AccessFeature PaperArticle

Towards Building the OP-Mapped WENO Schemes: A General Methodology

by Ruo Li and Wei Zhong

Math. Comput. Appl. 2021, 26(4), 67; https://doi.org/10.3390/mca26040067 - 23 Sep 2021

Cited by 5 | Viewed by 2135

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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