부산대학교 도서관

Summary: ``Moving interface problems are ubiquitous in science andengineering. To develop an accurate and efficient methodology for thisclass of problems, we present algorithms for local $h$-adaptivity ofhierarchical B-splines to be utilized in isogeometric analysis. Weextend Bézier projection, an efficient quadrature-free localprojection technique, to the hierarchical setting. In this case,extraction operators may not be invertible. To address this issue wedevelop a multi-level reconstruction operator which maintains thelocality properties of the projection. We also introduce a balanceparameter to control the overlap of hierarchical functions leading toimproved numerical conditioning. We apply our algorithms to thesimulation of localized prostate cancer growth. We model this diseaseusing the phase-field method and a set of diffusion-reaction equationsto account for the dynamics of nutrients and a key biomarker termedProstate Specific Antigen. Our results include examples on simple 2Dand 3D domains and a more compelling tissue-scale, patient-specificsimulation, which is run over a prostate anatomy extracted from medicalimages. Our methods for local $h$-adaptivity efficiently capture theevolving interface between the tumor and the neighboring healthy tissuewith remarkable accuracy in all cases.''