Adaptive mesh refinement (AMR) criteria comparison for the DrivAer model.

Aerodynamics is one of the main areas of development in vehicle design. One of the most efficient ways of testing the aerodynamic design of a vehicle is to use Computational Fluid Dynamics (CFD), which allows for faster and more accurate aerodynamic simulations, which in turn helps increase the fuel economy and electric vehicle's range. Resource optimization is one of the most important aspects of CFD, and one of its main aspects is the spatial discretization of the fluid domain. This study discusses the use of Adaptive Mesh Refinement (AMR) for the aerodynamic design of private vehicles. This paper compares the results obtained with the use of AMR based on different fluid dynamic criteria for the DrivAer model and correlates the results with experimental data and computational results provided by various authors in previous publications. Four different optimization functions are defined and compared. The results for the drag coefficient, pressure coefficient, and total pressure wake have been correlated, showing great accuracy. This study has proven that the use of AMR highly optimizes computational resources by optimizing the mesh in the desired areas, thereby reducing the number of cells needed elsewhere. The use of these criteria has proven useful for drag coefficient prediction simulations because these criteria make use of the AMR to optimize the wake region.

Real-time deformable SLAM with geometrically adapted template for dynamic monocular laparoscopic scenes.

PURPOSE: Intraoperative reconstruction of endoscopic scenes is a key technology for surgical navigation systems. The accuracy and efficiency of 3D reconstruction directly determine the effectiveness of navigation systems in a variety of clinical applications. While current deformable SLAM algorithms can meet real-time requirements, their underlying reliance on regular templates still makes it challenging to efficiently capture abrupt geometric features within scenes, such as organ contours and surgical margins. METHODS: We propose a novel real-time monocular deformable SLAM algorithm with geometrically adapted template. To ensure real-time performance, the proposed algorithm consists of two threads: a deformation mapping thread updates the template at keyframe rate and a deformation tracking thread estimates the camera pose and the deformation at frame rate. To capture geometric features more efficiently, the algorithm first detects salient edge features using a pre-trained contour detection network and then constructs the template through a triangulation method with guidance of the salient features. RESULTS: We thoroughly evaluated this method on Mandala and Hamlyn datasets in terms of accuracy and performance. The results demonstrated that the proposed method achieves better accuracy with 0.75-7.95% improvement and achieves consistent effectiveness in data association compared with the closest method. CONCLUSION: This study verified an adaptive template does improve the performance of reconstruction of dynamic laparoscopic Scenes with abrupt geometric features. However, further exploration is needed for applications in laparoscopic surgery with incisal margins caused by surgical instruments. This research serves as a crucial step toward enhanced automatic computer-assisted navigation in laparoscopic surgery. Code is available at https://github.com/Tang257/SLAM-with-geometrically-adapted-template .

Validation of a 3D Local-Scale Adaptive Solar Radiation Model by Using Pyranometer Measurements and a High-Resolution Digital Elevation Model.

The result of the multidisciplinary collaboration of researchers from different areas of knowledge to validate a solar radiation model is presented. The MAPsol is a 3D local-scale adaptive solar radiation model that allows us to estimate direct, diffuse, and reflected irradiance for clear sky conditions. The model includes the adaptation of the mesh to complex orography and albedo, and considers the shadows cast by the terrain and buildings. The surface mesh generation is based on surface refinement, smoothing and parameterization techniques and allows the generation of high-quality adapted meshes with a reasonable number of elements. Another key aspect of the paper is the generation of a high-resolution digital elevation model (DEM). This high-resolution DEM is constructed from LiDAR data, and its resolution is two times more accurate than the publicly available DEMs. The validation process uses direct and global solar irradiance data obtained from pyranometers at the University of Salamanca located in an urban area affected by systematic shading from nearby buildings. This work provides an efficient protocol for studying solar resources, with particular emphasis on areas of complex orography and dense buildings where shadows can potentially make solar energy production facilities less efficient.

An adaptive h-refinement method for the boundary element fast multipole method for quasi-static electromagnetic modeling.

Objective.In our recent work pertinent to modeling of brain stimulation and neurophysiological recordings, substantial modeling errors in the computed electric field and potential have sometimes been observed for standard multi-compartment head models. The goal of this study is to quantify those errors and, further, eliminate them through an adaptive mesh refinement (AMR) algorithm. The study concentrates on transcranial magnetic stimulation (TMS), transcranial electrical stimulation (TES), and electroencephalography (EEG) forward problems.Approach.We propose, describe, and systematically investigate an AMR method using the boundary element method with fast multipole acceleration (BEM-FMM) as the base numerical solver. The goal is to efficiently allocate additional unknowns to critical areas of the model, where they will best improve solution accuracy. The implemented AMR method's accuracy improvement is measured on head models constructed from 16 Human Connectome Project subjects under problem classes of TES, TMS, and EEG. Errors are computed between three solutions: an initial non-adaptive solution, a solution found after applying AMR with a conservative refinement rate, and a 'silver-standard' solution found by subsequent 4:1 global refinement of the adaptively-refined model.Main results.Excellent agreement is shown between the adaptively-refined and silver-standard solutions for standard head models. AMR is found to be vital for accurate modeling of TES and EEG forward problems for standard models: an increase of less than 25% (on average) in number of mesh elements for these problems, efficiently allocated by AMR, exposes electric field/potential errors exceeding 60% (on average) in the solution for the unrefined models.Significance.This error has especially important implications for TES dosing prediction-where the stimulation strength plays a central role-and for EEG lead fields. Though the specific form of the AMR method described here is implemented for the BEM-FMM, we expect that AMR is applicable and even required for accurate electromagnetic simulations by other numerical modeling packages as well.

Dynamic adaptive moving mesh finite-volume method for the blood flow and coagulation modeling.

In this work, we develop numerical methods for the solution of blood flow and coagulation on dynamic adaptive moving meshes. We consider the blood flow as a flow of incompressible Newtonian fluid governed by the Navier-Stokes equations. The blood coagulation is introduced through the additional Darcy term, with a permeability coefficient dependent on reactions. To this end, we introduce moving mesh collocated finite-volume methods for the Navier-Stokes equations, advection-diffusion equations, and a method for the stiff cascade of reactions. A monolithic nonlinear system is solved to advance the solution in time. The finite volume method for the Navier-Stokes equations features collocated arrangement of pressure and velocity unknowns and a coupled momentum and mass flux. The method is conservative and inf-sup stable despite the saddle point nature of the system. It is verified on a series of analytical problems and applied to the blood flow problem in the deforming domain of the right ventricle, reconstructed from a time series of computed tomography scans. At last, we demonstrate the ability to model the coagulation process in deforming microfluidic capillaries.

A Robust Adaptive Mesh Generation Algorithm: A Solution for Simulating 2D Crack Growth Problems.

This paper introduces a robust algorithm that efficiently generates high-quality unstructured triangular meshes to model complex two-dimensional crack growth problems within the framework of linear elastic fracture mechanics (LEFM). The proposed Visual Fortran code aims to address key challenges in mesh generation including geometric complexity, required simulation accuracy, and computational resource constraints. The algorithm incorporates adaptive refinement and updates to the mesh structure near the crack tip, resulting in the formation of rosette elements that provide accurate approximations of stress intensity factors (SIFs). By utilizing the maximum circumferential stress theory, the algorithm predicts the new crack path based on these SIFs. Throughout the simulation of crack propagation, a node splitting approach was employed to represent the progression of the crack, while the crack growth path is determined by successive linear extensions for each crack growth increment. To compute stress intensity factors (SIFs) for each increment of crack extension, a displacement extrapolation method was used. The experimental and numerical results demonstrated the algorithm's effectiveness in accurately predicting crack growth and facilitating reliable stress analysis for complex crack growth problems in two dimensions. The obtained results for the SIF were found to be consistent with other analytical solutions for standard geometries.

Adaptive octree meshes for simulation of extracellular electrophysiology.

Objective.The interaction between neural tissues and artificial electrodes is crucial for understanding and advancing neuroscientific research and therapeutic applications. However, accurately modeling this space around the neurons rapidly increases the computational complexity of neural simulations.Approach.This study demonstrates a dynamically adaptive simulation method that greatly accelerates computation by adjusting spatial resolution of the simulation as needed. Use of an octree structure for the mesh, in combination with the admittance method for discretizing conductivity, provides both accurate approximation and ease of modification on-the-fly.Main results.In tests of both local field potential estimation and multi-electrode stimulation, dynamically adapted meshes achieve accuracy comparable to high-resolution static meshes in an order of magnitude less time.Significance.The proposed simulation pipeline improves model scalability, allowing greater detail with fewer computational resources. The implementation is available as an open-source Python module, providing flexibility and ease of reuse for the broader research community.

An Adaptive H-Refinement Method for the Boundary Element Fast Multipole Method for Quasi-static Electromagnetic Modeling.

Objective: In our recent work pertinent to modeling of brain stimulation and neurophysiological recordings, substantial modeling errors in the computed electric field and potential have sometimes been observed for standard multi-compartment head models. The goal of this study is to quantify those errors and, further, eliminate them through an adaptive mesh refinement (AMR) algorithm. The study concentrates on transcranial magnetic stimulation (TMS), transcranial electrical stimulation (TES), and electroencephalography (EEG) forward problems. Approach: We propose, describe, and systematically investigate an AMR method using the Boundary Element Method with Fast Multipole Acceleration (BEM-FMM) as the base numerical solver. The goal is to efficiently allocate additional unknowns to critical areas of the model, where they will best improve solution accuracy.The implemented AMR method's accuracy improvement is measured on head models constructed from 16 Human Connectome Project subjects under problem classes of TES, TMS, and EEG. Errors are computed between three solutions: an initial non-adaptive solution, a solution found after applying AMR with a conservative refinement rate, and a "silver-standard" solution found by subsequent 4:1 global refinement of the adaptively-refined model. Main Results: Excellent agreement is shown between the adaptively-refined and silver-standard solutions for standard head models. AMR is found to be vital for accurate modeling of TES and EEG forward problems for standard models: an increase of less than 25% (on average) in number of mesh elements for these problems, efficiently allocated by AMR, exposes electric field/potential errors exceeding 60% (on average) in the solution for the unrefined models. Significance: This error has especially important implications for TES dosing prediction - where the stimulation strength plays a central role - and for EEG lead fields. Though the specific form of the AMR method described here is implemented for the BEM-FMM, we expect that AMR is applicable and even required for accurate electromagnetic simulations by other numerical modeling packages as well.

An adaptive semi-implicit finite element solver for brain cancer progression modeling.

Glioblastoma is the most aggressive and infiltrative glioma, classified as Grade IV, with the poorest survival rate among patients. Accurate and rigorously tested mechanistic in silico modeling offers great value to understand and quantify the progression of primary brain tumors. This paper presents a continuum-based finite element framework that is built on high performance computing, open-source libraries to simulate glioblastoma progression. We adopt the established proliferation invasion hypoxia necrosis angiogenesis model in our framework to realize scalable simulations of cancer, and has demonstrated to produce accurate and efficient solutions in both two- and three-dimensional brain models. The in silico solver can successfully implement arbitrary order discretization schemes and adaptive remeshing algorithms. A model sensitivity analysis is conducted to test the impact of vascular density, cancer cell invasiveness and aggressiveness, the phenotypic transition potential, including that of necrosis, and the effect of tumor-induced angiogenesis in the evolution of glioblastoma. Additionally, individualized simulations of brain cancer progression are carried out using pertinent magnetic resonance imaging data, where the in silico model is used to investigate the complex dynamics of the disease. We conclude by arguing how the proposed framework can deliver patient-specific simulations of cancer prognosis and how it could bridge clinical imaging with modeling.

Adaptive Finite Element Modeling of Linear Elastic Fatigue Crack Growth.

This paper proposed an efficient two-dimensional fatigue crack growth simulation program for linear elastic materials using an incremental crack growth procedure. The Visual Fortran programming language was used to develop the finite element code. The adaptive finite element mesh was generated using the advancing front method. Stress analysis for each increment was carried out using the adaptive mesh finite element technique. The equivalent stress intensity factor is the most essential parameter that should be accurately estimated for the mixed-mode loading condition which was used as the onset criterion for the crack growth. The node splitting and relaxation method advances the crack once the failure mechanism and crack direction have been determined. The displacement extrapolation technique (DET) was used to calculate stress intensity factors (SIFs) at each crack extension increment. Then, these SIFs were analyzed using the maximum circumferential stress theory (MCST) to predict the crack propagation trajectory and the fatigue life cycles using the Paris' law model. Finally, the performance and capability of the developed program are shown in the application examples.

Enhanced 4D Flow MRI-Based CFD with Adaptive Mesh Refinement for Flow Dynamics Assessment in Coarctation of the Aorta.

4D Flow MRI is a diagnostic tool that can visualize and quantify patient-specific hemodynamics and help interventionalists optimize treatment strategies for repairing coarctation of the aorta (COA). Despite recent developments in 4D Flow MRI, shortcomings include phase-offset errors, limited spatiotemporal resolution, aliasing, inaccuracies due to slow aneurysmal flows, and distortion of images due to metallic artifact from vascular stents. To address these limitations, we developed a framework utilizing Computational Fluid Dynamics (CFD) with Adaptive Mesh Refinement (AMR) that enhances 4D Flow MRI visualization/quantification. We applied this framework to five pediatric patients with COA, providing in-vivo and in-silico datasets, pre- and post-intervention. These two data sets were compared and showed that CFD flow rates were within 9.6% of 4D Flow MRI, which is within a clinically acceptable range. CFD simulated slow aneurysmal flow, which MRI failed to capture due to high relative velocity encoding (Venc). CFD successfully predicted in-stent blood flow, which was not visible in the in-vivo data due to susceptibility artifact. AMR improved spatial resolution by factors of 101 to 103 and temporal resolution four-fold. This computational framework has strong potential to optimize visualization/quantification of aneurysmal and in-stent flows, improve spatiotemporal resolution, and assess hemodynamic efficiency post-COA treatment.

Dynamic mode decomposition in adaptive mesh refinement and coarsening simulations.

Dynamic mode decomposition (DMD) is a powerful data-driven method used to extract spatio-temporal coherent structures that dictate a given dynamical system. The method consists of stacking collected temporal snapshots into a matrix and mapping the nonlinear dynamics using a linear operator. The classical procedure considers that snapshots possess the same dimensionality for all the observable data. However, this often does not occur in numerical simulations with adaptive mesh refinement/coarsening schemes (AMR/C). This paper proposes a strategy to enable DMD to extract features from observations with different mesh topologies and dimensions, such as those found in AMR/C simulations. For this purpose, the adaptive snapshots are projected onto the same reference function space, enabling the use of snapshot-based methods such as DMD. The present strategy is applied to challenging AMR/C simulations: a continuous diffusion-reaction epidemiological model for COVID-19, a density-driven gravity current simulation, and a bubble rising problem. We also evaluate the DMD efficiency to reconstruct the dynamics and some relevant quantities of interest. In particular, for the SEIRD model and the bubble rising problem, we evaluate DMD's ability to extrapolate in time (short-time future estimates).

Investigation the effect of geometry and position of polymeric heart valves on hemodynamic with fluid-structure interaction numerical method.

Computational modeling and numerical simulation of heart valve dynamics incorporating both fluid dynamics and valve structural replications has been challenging. In this study, we developed a double-coupled fluid-structure interaction (FSI) model using arbitrary lagrangian eulerian(ALE) and steered adaptive mesh(SAM). So we were looking to simulate transcatheter aortic valve (TAV) hemodynamic performance throughout entire cardiac cycles [1]. To reach this object, semi-real geometry of aorta and aortic polymeric valves has been created. At model inlet, left ventricular pressure and at the model outlet the elastic porous tube have been considered. Nonlinear finite element way and Sparse solver was utilized to couple fluid and solid equation. Consequently, extensive and comparative simulation were performed to investigate the impact of valve elasticity and valve positions on hemodynamics and solid parameters. Effective Orifice Area(EOA) also has been calculated [1]. The simulation results indicated that the lower of the elastic modulus cause to increase the EOA. Furthermore, the result of valve position showed, whenever the valve is closer to sinuses, a greater EOA and lower stresses impose on the leaflet are achievable.

Adaptive Finite Element Model for Simulating Crack Growth in the Presence of Holes.

This study presents a developed finite element code written by Visual Fortran to computationally model fatigue crack growth (FCG) in arbitrary 2D structures with constant amplitude loading, using the linear elastic fracture mechanics (LEFM) concept. Accordingly, optimizing an FCG analysis, it is necessary to describe all the characteristics of the 2D model of the cracked component, including loads, support conditions, and material characteristics. The advancing front method has been used to generate the finite element mesh. The equivalent stress intensity factor was used as the onset criteria of crack propagation, since it is the main significant parameter that must be precisely predicted. As such, a criterion premised on direction (maximum circumferential stress theory) was implemented. After pre-processing, the analysis continues with incremental analysis of the crack growth, which is discretized into short straight segments. The adaptive mesh finite element method was used to perform the stress analysis for each increment. The displacement extrapolation technique was employed at each crack extension increment to compute the SIFs, which are then assessed by the maximum circumferential stress theory to determine the direction of the crack growth and predict the fatigue life as a function of crack length using a modified form of Paris' law. The application examples demonstrate the developed program's capability and performance.

Adaptive mesh refinement and coarsening for diffusion-reaction epidemiological models.

The outbreak of COVID-19 in 2020 has led to a surge in the interest in the mathematical modeling of infectious diseases. Disease transmission may be modeled as compartmental models, in which the population under study is divided into compartments and has assumptions about the nature and time rate of transfer from one compartment to another. Usually, they are composed of a system of ordinary differential equations in time. A class of such models considers the Susceptible, Exposed, Infected, Recovered, and Deceased populations, the SEIRD model. However, these models do not always account for the movement of individuals from one region to another. In this work, we extend the formulation of SEIRD compartmental models to diffusion-reaction systems of partial differential equations to capture the continuous spatio-temporal dynamics of COVID-19. Since the virus spread is not only through diffusion, we introduce a source term to the equation system, representing exposed people who return from travel. We also add the possibility of anisotropic non-homogeneous diffusion. We implement the whole model in libMesh, an open finite element library that provides a framework for multiphysics, considering adaptive mesh refinement and coarsening. Therefore, the model can represent several spatial scales, adapting the resolution to the disease dynamics. We verify our model with standard SEIRD models and show several examples highlighting the present model's new capabilities.

Efficient mesh refinement for the Poisson-Boltzmann equation with boundary elements.

The Poisson-Boltzmann equation is a widely used model to study electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate representations of the solute, which is usually a complicated geometry. Here, we utilize adjoint-based analyses to form two goal-oriented error estimates that allow us to determine the contribution of each discretization element (panel) to the numerical error in the solvation free energy. This information is useful to identify high-error panels to then refine them adaptively to find optimal surface meshes. We present results for spheres and real molecular geometries, and see that elements with large error tend to be in regions where there is a high electrostatic potential. We also find that even though both estimates predict different total errors, they have similar performance as part of an adaptive mesh refinement scheme. Our test cases suggest that the adaptive mesh refinement scheme is very effective, as we are able to reduce the error one order of magnitude by increasing the mesh size less than 20% and come out to be more efficient than uniform refinement when computing error estimations. This result sets the basis toward efficient automatic mesh refinement schemes that produce optimal meshes for solvation energy calculations.

Softness-based adaptive mesh refinement algorithm for soft tissue deformation.

Soft tissue and organ modeling is the most critical function of any virtual surgical system. This study proposes a softness-based adaptive mesh refinement algorithm to simultaneously ensure realistic and real-time soft tissue simulation. The algorithm was constructed to consider that in a virtual surgery scenario, the surgical sites involve large deformation and thus require high simulation precision, whereas the nonsurgical sites involve small deformations and thus require low simulation precision. This study used the stomach lining as an example, applying mesh refinement in the deformation sites of the stomach lining to enhance the accuracy of the simulations. In addition, low mesh models were adopted for nonsurgical sites to ensure computing efficiency.

Accuracy Quantification of the Reverse Engineering and High-Order Finite Element Analysis of Equine MC3 Forelimb.

Shape is a key factor in influencing mechanical responses of bones. Considered to be smart viscoelastic and inhomogeneous materials, bones are stimulated to change shape (model and remodel) when they experience changes in the compressive strain distribution. Using reverse engineering techniques via computer-aided design (CAD) is crucial to create a virtual environment to investigate the significance of shape in biomechanical engineering. Nonetheless, data are lacking to quantify the accuracy of generated models and to address errors in finite element analysis (FEA). In the present study, reverse engineering through extrapolating cross-sectional slices was used to reconstruct the diaphysis of 15 equine third metacarpal bones (MC3). The reconstructed geometry was aligned with, and compared against, computed tomography-based models (reference models) of these bones and then the error map of the generated surfaces was plotted. The minimum error of reconstructed geometry was found to be +0.135 mm and -0.185 mm (0.407 mm ± 0.235, P > .05 and -0.563 mm ± 0.369, P > .05 for outside [convex] and inside [concave] surface position, respectively). Minor reconstructed surface error was observed on the dorsal cortex (0.216 mm ± 0.07, P > .05) for the outside surface and -0.185 mm ± 0.13, P > .05 for the inside surface. In addition, a displacement-based error estimation was used on 10 MC3 to identify poorly shaped elements in FEA, and the relations of finite element convergence analysis were used to present a framework for minimizing stress and strain errors in FEA. Finite element analysis errors of 3%-5% provided in the literature are unfortunate. Our proposed model, which presents an accurate FEA (error of 0.12%) in the smallest number of iterations possible, will assist future investigators to maximize FEA accuracy without the current runtime penalty.

New Strategy for Finite Element Mesh Generation for Accurate Solutions of Electroencephalography Forward Problems.

The finite element method (FEM) is a numerical method that is often used for solving electroencephalography (EEG) forward problems involving realistic head models. In this study, FEM solutions obtained using three different mesh structures, namely coarse, densely refined, and adaptively refined meshes, are compared. The simulation results showed that the accuracy of FEM solutions could be significantly enhanced by adding a small number of elements around regions with large estimated errors. Moreover, it was demonstrated that the adaptively refined regions were always near the current dipole sources, suggesting that selectively generating additional elements around the cortical surface might be a new promising strategy for more efficient FEM-based EEG forward analysis.

OpenIFEM: A High Performance Modular Open-Source Software of the Immersed Finite Element Method for Fluid-Structure Interactions.

We present a high performance modularly-built open-source software - OpenIFEM. OpenIFEM is a C++ implementation of the modified immersed finite element method (mIFEM) to solve fluid-structure interaction (FSI) problems. This software is modularly built to perform multiple tasks including fluid dynamics (incompressible and slightly compressible fluid models), linear and nonlinear solid mechanics, and fully coupled fluid-structure interactions. Most of open-source software packages are restricted to certain discretization methods; some are under-tested, under-documented, and lack modularity as well as extensibility. OpenIFEM is designed and built to include a set of generic classes for users to adapt so that any fluid and solid solvers can be coupled through the FSI algorithm. In addition, the package utilizes well-developed and tested libraries. It also comes with standard test cases that serve as software and algorithm validation. The software can be built on cross-platform, i.e., Linux, Windows, and Mac OS, using CMake. Efficient parallelization is also implemented for high-performance computing for large-sized problems. OpenIFEM is documented using Doxygen and publicly available to download on GitHub. It is expected to benefit the future development of FSI algorithms and be applied to a variety of FSI applications.