Isogeometric FEM-BEM coupled structural-acoustic analysis of shells using subdivision surfaces

We introduce a coupled finite and boundary element formulation for acoustic scattering analysis over thin shell structures. A triangular Loop subdivision surface discretisation is used for both geometry and analysis fields. The Kirchhoff-Love shell equation is discretised with the finite element method and the Helmholtz equation for the acoustic field with the boundary element method. The use of the boundary element formulation allows the elegant handling of infinite domains and precludes the need for volumetric meshing. In the present work the subdivision control meshes for the shell displacements and the acoustic pressures have the same resolution. The corresponding smooth subdivision basis functions have the $C^1$ continuity property required for the Kirchhoff-Love formulation and are highly efficient for the acoustic field computations. We validate the proposed isogeometric formulation through a closed-form solution of acoustic scattering over a thin shell sphere. Furthermore, we demonstrate the ability of the proposed approach to handle complex geometries with arbitrary topology that provides an integrated isogeometric design and analysis workflow for coupled structural-acoustic analysis of shells

Isogeometric FEM-BEM coupled structural-acoustic analysis of shells using subdivision surfaces

We introduce a coupled finite and boundary element formulation for acoustic scattering analysis over thin shell structures. A triangular Loop subdivision surface discretisation is used for both geometry and analysis fields. The Kirchhoff-Love shell equation is discretised with the finite element method and the Helmholtz equation for the acoustic field with the boundary element method. The use of the boundary element formulation allows the elegant handling of infinite domains and precludes the need for volumetric meshing. In the present work the subdivision control meshes for the shell displacements and the acoustic pressures have the same resolution. The corresponding smooth subdivision basis functions have the $C^1$ continuity property required for the Kirchhoff-Love formulation and are highly efficient for the acoustic field computations. We validate the proposed isogeometric formulation through a closed-form solution of acoustic scattering over a thin shell sphere. Furthermore, we demonstrate the ability of the proposed approach to handle complex geometries with arbitrary topology that provides an integrated isogeometric design and analysis workflow for coupled structural-acoustic analysis of shells

CLASSIFICATION OF NEUROANATOMICAL STRUCTURES BASED ON NON-EUCLIDEAN GEOMETRIC OBJECT PROPERTIES

Studying the observed morphological differences in neuroanatomical structures between individuals with neurodevelopmental disorders and a control group of typically developing individuals has been an important objective. Researchers study the differences with two goals: to assist an accurate diagnosis of the disease and to gain insights into underlying mechanisms of the disease that cause such changes. Shape classification is commonly utilized in such studies. An effective classification is difficult because it requires 1) a choice of an object model that can provide rich geometric object properties (GOPs) relevant for a given classification task, and 2) a choice of a statistical classification method that accounts for the non-Euclidean nature of GOPs. I lay out my methodological contributions to address the aforementioned challenges in the context of early diagnosis and detection of Autism Spectrum Disorder (ASD) in infants based on shapes of hippocampi and caudate nuclei; morphological deviations in these structures between individuals with ASD and typically developing individuals have been reported in the literature. These contributions respectively lead to 1) an effective modeling of shapes of objects of interest and 2) an effective classification. As the first contribution for modeling shapes of objects, I propose a method to obtain a set of skeletal models called s-reps from a set of 3D objects. First, the method iteratively deforms the object surface via Mean Curvature Flow (MCF) until the deformed surface is approximately ellipsoidal. Then, an s-rep of the approximate ellipsoid is obtained analytically. Finally, the ellipsoid s-rep is deformed via a series of inverse MCF transformations. The method has two important properties: 1) it is fully automatic, and 2) it yields a set of s-reps with good correspondence across the set. The method is shown effective in generating a set of s-reps for a few neuroanatomical structures. As the second contribution with respect to modeling shapes of objects, I introduce an extension to the current s-rep for representing an object with a narrowing sharp tail. This includes a spoke interpolation method for interpolating a discrete s-rep of an object with a narrowing sharp tail into a continuous object. This extension is necessary for representing surface geometry of objects whose boundary has a singular point. I demonstrate that this extension allows appropriate surface modeling of a narrowing sharp tail region of the caudate nucleus. In addition, I show that the extension is beneficial in classifying autistic and non-autistic infants at high risk of ASD based on shapes of caudate nuclei. As the first contribution with respect to statistical methods, I propose a novel shape classification framework that uses the s-rep to capture rich localized geometric descriptions of an object, a statistical method called Principal Nested Spheres (PNS) analysis to handle the non-Euclidean s-rep GOPs, and a classification method called Distance Weighted Discrimination (DWD). I evaluate the effectiveness of the proposed method in classifying autistic and non-autistic infants based on either hippocampal shapes or caudate shapes in terms of the Area Under the ROC curve (AUC). In addition, I show that the proposed method is superior to commonly used shape classification methods in the literature. As my final methodological contribution, I extend the proposed shape classification method to perform the classifcation task based on temporal shape differences. DWD learns a class separation direction based on the temporal shape differences that are obtained by taking differences of the temporal pair of Euclideanized s-reps. In the context of early diagnosis and detection of ASD in young infants, the proposed temporal shape difference classification produces some interesting results; the temporal differences in shapes of hippocampi and caudate nuclei do not seem to be as predictive as the cross-sectional shape of these structures alone.Doctor of Philosoph