Coral reefs cover an area of over 280, 000km2 and support thousands of species in what many descr... more Coral reefs cover an area of over 280, 000km2 and support thousands of species in what many describe as the “rain forests of the seas”. Coral reefs face numerous threats, with current estimates suggesting that thirty percent of corals are in critical condition and may die within 10 to 20 years [cite]. One resourceful way to monitor the health of a coral reef is to periodically take aerial images of the reef from a UAV, use these images to construct a 3D model of the reef and monitor its evolution in time. Here we present a methodology for the 3D reconstruction, segmentation and classification of corals form aerial images taken by an UAV. The proposed methodology consists of building 3D point cloud from the images based on “structure from motion ” approach, and then building the 3D surface to fit the point cloud. We segment the 3D surface based on the discrete mean curvature of the surface, cluster the coral containing segment into groups of individual corals using mean-shift algorit...
ABSTRACTThe novel coronavirus disease (COVID-19) has caused a pandemic that has disrupted supply ... more ABSTRACTThe novel coronavirus disease (COVID-19) has caused a pandemic that has disrupted supply chains globally. This black swan event is challenging industries from all sectors of the economy including those industries directly needed to produce items that safeguard us from the disease itself, especially personal protection equipment (N95 masks, face shields) and much needed consumables associated with testing and vaccine delivery (swabs, vials and viral transfer medium). Digital manufacturing, especially 3D printing, has been promulgated as an important approach for the rapid development of new products as well as a replacement manufacturing technique for many traditional manufacturing methods, including injection molding, when supply chains are disrupted. Herein we report the use of Digital Light Synthesis (DLS) for the design and large-scale deployment of nasopharyngeal (NP) swabs for testing of coronavirus SARS-CoV-2 infections in humans. NP swabs have been one of society’s es...
Innovative Numerical Approaches for Multi-Field and Multi-Scale Problems, 2016
Universal meshes have recently appeared in the literature as a computationally efficient and robu... more Universal meshes have recently appeared in the literature as a computationally efficient and robust paradigm for the generation of conforming simplicial meshes for domains with evolving boundaries. The main idea behind a universal mesh is to immerse the moving boundary in a background mesh (the universal mesh), and to produce a mesh that conforms to the moving boundary at any given time by adjusting a few of elements of the background mesh. In this manuscript we present the application of universal meshes to the simulation of brittle fracturing. To this extent, we provide a high level description of a crack propagation algorithm and showcase its capabilities. Alongside universal meshes for the simulation of brittle fracture, we provide other examples for which universal meshes prove to be a powerful tool, namely fluid flow past moving obstacles. Lastly, we conclude the manuscript with some remarks on the current state of universal meshes and future directions. Dedicated to Michael Ortiz on the occasion of his 60 th birthday.
International Journal for Numerical Methods in Engineering, 2018
We describe an algorithm to recover a boundary-fitting triangulation for a bounded C 2-regular do... more We describe an algorithm to recover a boundary-fitting triangulation for a bounded C 2-regular domain Ω ⊂ R 3 immersed in a nonconforming background mesh of tetrahedra. The algorithm consists in identifying a polyhedral domain h bounded by facets in the background mesh and morphing h into a boundary-fitting polyhedral approximation Ω h of Ω. We discuss assumptions on the regularity of the domain, on element sizes and on specific angles in the background mesh that appear to render the algorithm robust. With the distinctive feature of involving just small perturbations of a few elements of the background mesh that are in the vicinity of the immersed boundary, the algorithm is designed to benefit numerical schemes for simulating free and moving boundary problems. In such problems, it is now possible to immerse an evolving geometry in the same background mesh, called a universal mesh, and recover conforming discretizations for it. In particular, the algorithm entirely avoids remeshing-type operations and its complexity scales approximately linearly with the number of elements in the vicinity of the immersed boundary. We include detailed examples examining its performance.
We describe a method for discretizing C continuous surface(s) in R immersed in a non-conforming t... more We describe a method for discretizing C continuous surface(s) in R immersed in a non-conforming tetrahedralization. The method consists of constructing a homeomorphic mapping from the tetrahedrons in a background mesh to ones conforming to the immersed geometry. Such a map relies on the way we parametrize the surface(s) of the immersed geometry over a collection of a nearby triangular faces with their closest point projections. In order to guarantee existence of such a parametrization of a surface, we need to impose restrictions on the background mesh. These restrictions define a family of surfaces that can be parametrized with a given background mesh.
Computer Methods in Applied Mechanics and Engineering, 2015
Computational modeling of thin biological membranes can aid the design of better medical devices.... more Computational modeling of thin biological membranes can aid the design of better medical devices. Remarkable biological membranes include skin, alveoli, blood vessels, and heart valves. Isogeometric analysis is ideally suited for biological membranes since it inherently satisfies the C 1-requirement for Kirchhoff-Love kinematics. Yet, current isogeometric shell formulations are mainly focused on linear isotropic materials, while biological tissues are characterized by a nonlinear anisotropic stress-strain response. Here we present a thin shell formulation for thin biological membranes. We derive the equilibrium equations using curvilinear convective coordinates on NURBS tensor product surface patches. We linearize the weak form of the generic linear momentum balance without a particular choice of a constitutive law. We then incorporate the constitutive equations that have been designed specifically for collagenous tissues. We explore three common anisotropic material models: Mooney-Rivlin, May Newmann-Yin, and Gasser-Ogden-Holzapfel. Our work will allow scientists in biomechanics and mechanobiology to adopt the constitutive equations that have been developed for solid three-dimensional soft tissues within the framework of isogeometric thin shell analysis.
International Journal for Numerical Methods in Engineering, 2015
We propose a family of methods for simulating two-dimensional incompressible, low Reynolds number... more We propose a family of methods for simulating two-dimensional incompressible, low Reynolds number flow around a moving obstacle whose motion is prescribed. The methods make use of a universal mesh: a fixed background mesh that adapts to the geometry of the immersed obstacle at all times by adjusting a few elements in the neighborhood of the obstacle's boundary. The resulting mesh provides a conforming triangulation of the fluid domain over which discretizations of any desired order of accuracy in space and time can be constructed using standard finite element spaces together with off-the-shelf time integrators. We demonstrate the approach by using Taylor-Hood elements to approximate the fluid velocity and pressure. To integrate in time, we consider implicit Runge-Kutta schemes as well as a fractional step scheme. We illustrate the methods and study their convergence numerically via examples that involve flow around obstacles that undergo prescribed deformations.
Computer Methods in Applied Mechanics and Engineering, 2015
Highlights • An HDG method for nonlinear elasticity based on a minimum principle is presented. • ... more Highlights • An HDG method for nonlinear elasticity based on a minimum principle is presented. • An example is shown in which the method fails to converge to the exact solution. • Examples of the performance of the method in demanding 3D cases are shown. • Presented metrics comparing efficiency of HDG compare to CG and DG methods.
In many engineering applications, it is common to solve sequences of linear systems of the form A... more In many engineering applications, it is common to solve sequences of linear systems of the form A(n)x(n) = b(n), n = 0, 1, 2,..., (1) via Krylov subspace methods, where the A(n)’s are sparse, nonsymmetric ma-
Coral reefs cover an area of over 280, 000km and support thousands of species in what many descri... more Coral reefs cover an area of over 280, 000km and support thousands of species in what many describe as the “rain forests of the seas”. Coral reefs face numerous threats, with current estimates suggesting that thirty percent of corals are in critical condition and may die within 10 to 20 years [cite]. One resourceful way to monitor the health of a coral reef is to periodically take aerial images of the reef from a UAV, use these images to construct a 3D model of the reef and monitor its evolution in time. Here we present a methodology for the 3D reconstruction, segmentation and classification of corals form aerial images taken by an UAV. The proposed methodology consists of building 3D point cloud from the images based on “structure from motion” approach, and then building the 3D surface to fit the point cloud. We segment the 3D surface based on the discrete mean curvature of the surface, cluster the coral containing segment into groups of individual corals using mean-shift algorithm...
Coral reefs cover an area of over 280, 000km2 and support thousands of species in what many descr... more Coral reefs cover an area of over 280, 000km2 and support thousands of species in what many describe as the “rain forests of the seas”. Coral reefs face numerous threats, with current estimates suggesting that thirty percent of corals are in critical condition and may die within 10 to 20 years [cite]. One resourceful way to monitor the health of a coral reef is to periodically take aerial images of the reef from a UAV, use these images to construct a 3D model of the reef and monitor its evolution in time. Here we present a methodology for the 3D reconstruction, segmentation and classification of corals form aerial images taken by an UAV. The proposed methodology consists of building 3D point cloud from the images based on “structure from motion ” approach, and then building the 3D surface to fit the point cloud. We segment the 3D surface based on the discrete mean curvature of the surface, cluster the coral containing segment into groups of individual corals using mean-shift algorit...
ABSTRACTThe novel coronavirus disease (COVID-19) has caused a pandemic that has disrupted supply ... more ABSTRACTThe novel coronavirus disease (COVID-19) has caused a pandemic that has disrupted supply chains globally. This black swan event is challenging industries from all sectors of the economy including those industries directly needed to produce items that safeguard us from the disease itself, especially personal protection equipment (N95 masks, face shields) and much needed consumables associated with testing and vaccine delivery (swabs, vials and viral transfer medium). Digital manufacturing, especially 3D printing, has been promulgated as an important approach for the rapid development of new products as well as a replacement manufacturing technique for many traditional manufacturing methods, including injection molding, when supply chains are disrupted. Herein we report the use of Digital Light Synthesis (DLS) for the design and large-scale deployment of nasopharyngeal (NP) swabs for testing of coronavirus SARS-CoV-2 infections in humans. NP swabs have been one of society’s es...
Innovative Numerical Approaches for Multi-Field and Multi-Scale Problems, 2016
Universal meshes have recently appeared in the literature as a computationally efficient and robu... more Universal meshes have recently appeared in the literature as a computationally efficient and robust paradigm for the generation of conforming simplicial meshes for domains with evolving boundaries. The main idea behind a universal mesh is to immerse the moving boundary in a background mesh (the universal mesh), and to produce a mesh that conforms to the moving boundary at any given time by adjusting a few of elements of the background mesh. In this manuscript we present the application of universal meshes to the simulation of brittle fracturing. To this extent, we provide a high level description of a crack propagation algorithm and showcase its capabilities. Alongside universal meshes for the simulation of brittle fracture, we provide other examples for which universal meshes prove to be a powerful tool, namely fluid flow past moving obstacles. Lastly, we conclude the manuscript with some remarks on the current state of universal meshes and future directions. Dedicated to Michael Ortiz on the occasion of his 60 th birthday.
International Journal for Numerical Methods in Engineering, 2018
We describe an algorithm to recover a boundary-fitting triangulation for a bounded C 2-regular do... more We describe an algorithm to recover a boundary-fitting triangulation for a bounded C 2-regular domain Ω ⊂ R 3 immersed in a nonconforming background mesh of tetrahedra. The algorithm consists in identifying a polyhedral domain h bounded by facets in the background mesh and morphing h into a boundary-fitting polyhedral approximation Ω h of Ω. We discuss assumptions on the regularity of the domain, on element sizes and on specific angles in the background mesh that appear to render the algorithm robust. With the distinctive feature of involving just small perturbations of a few elements of the background mesh that are in the vicinity of the immersed boundary, the algorithm is designed to benefit numerical schemes for simulating free and moving boundary problems. In such problems, it is now possible to immerse an evolving geometry in the same background mesh, called a universal mesh, and recover conforming discretizations for it. In particular, the algorithm entirely avoids remeshing-type operations and its complexity scales approximately linearly with the number of elements in the vicinity of the immersed boundary. We include detailed examples examining its performance.
We describe a method for discretizing C continuous surface(s) in R immersed in a non-conforming t... more We describe a method for discretizing C continuous surface(s) in R immersed in a non-conforming tetrahedralization. The method consists of constructing a homeomorphic mapping from the tetrahedrons in a background mesh to ones conforming to the immersed geometry. Such a map relies on the way we parametrize the surface(s) of the immersed geometry over a collection of a nearby triangular faces with their closest point projections. In order to guarantee existence of such a parametrization of a surface, we need to impose restrictions on the background mesh. These restrictions define a family of surfaces that can be parametrized with a given background mesh.
Computer Methods in Applied Mechanics and Engineering, 2015
Computational modeling of thin biological membranes can aid the design of better medical devices.... more Computational modeling of thin biological membranes can aid the design of better medical devices. Remarkable biological membranes include skin, alveoli, blood vessels, and heart valves. Isogeometric analysis is ideally suited for biological membranes since it inherently satisfies the C 1-requirement for Kirchhoff-Love kinematics. Yet, current isogeometric shell formulations are mainly focused on linear isotropic materials, while biological tissues are characterized by a nonlinear anisotropic stress-strain response. Here we present a thin shell formulation for thin biological membranes. We derive the equilibrium equations using curvilinear convective coordinates on NURBS tensor product surface patches. We linearize the weak form of the generic linear momentum balance without a particular choice of a constitutive law. We then incorporate the constitutive equations that have been designed specifically for collagenous tissues. We explore three common anisotropic material models: Mooney-Rivlin, May Newmann-Yin, and Gasser-Ogden-Holzapfel. Our work will allow scientists in biomechanics and mechanobiology to adopt the constitutive equations that have been developed for solid three-dimensional soft tissues within the framework of isogeometric thin shell analysis.
International Journal for Numerical Methods in Engineering, 2015
We propose a family of methods for simulating two-dimensional incompressible, low Reynolds number... more We propose a family of methods for simulating two-dimensional incompressible, low Reynolds number flow around a moving obstacle whose motion is prescribed. The methods make use of a universal mesh: a fixed background mesh that adapts to the geometry of the immersed obstacle at all times by adjusting a few elements in the neighborhood of the obstacle's boundary. The resulting mesh provides a conforming triangulation of the fluid domain over which discretizations of any desired order of accuracy in space and time can be constructed using standard finite element spaces together with off-the-shelf time integrators. We demonstrate the approach by using Taylor-Hood elements to approximate the fluid velocity and pressure. To integrate in time, we consider implicit Runge-Kutta schemes as well as a fractional step scheme. We illustrate the methods and study their convergence numerically via examples that involve flow around obstacles that undergo prescribed deformations.
Computer Methods in Applied Mechanics and Engineering, 2015
Highlights • An HDG method for nonlinear elasticity based on a minimum principle is presented. • ... more Highlights • An HDG method for nonlinear elasticity based on a minimum principle is presented. • An example is shown in which the method fails to converge to the exact solution. • Examples of the performance of the method in demanding 3D cases are shown. • Presented metrics comparing efficiency of HDG compare to CG and DG methods.
In many engineering applications, it is common to solve sequences of linear systems of the form A... more In many engineering applications, it is common to solve sequences of linear systems of the form A(n)x(n) = b(n), n = 0, 1, 2,..., (1) via Krylov subspace methods, where the A(n)’s are sparse, nonsymmetric ma-
Coral reefs cover an area of over 280, 000km and support thousands of species in what many descri... more Coral reefs cover an area of over 280, 000km and support thousands of species in what many describe as the “rain forests of the seas”. Coral reefs face numerous threats, with current estimates suggesting that thirty percent of corals are in critical condition and may die within 10 to 20 years [cite]. One resourceful way to monitor the health of a coral reef is to periodically take aerial images of the reef from a UAV, use these images to construct a 3D model of the reef and monitor its evolution in time. Here we present a methodology for the 3D reconstruction, segmentation and classification of corals form aerial images taken by an UAV. The proposed methodology consists of building 3D point cloud from the images based on “structure from motion” approach, and then building the 3D surface to fit the point cloud. We segment the 3D surface based on the discrete mean curvature of the surface, cluster the coral containing segment into groups of individual corals using mean-shift algorithm...
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