학술논문
Hierarchically refined and coarsened splines for moving interface problems, with particular application to phase-field models of prostate tumor growth.
Document Type
Journal
Author
Lorenzo, G. (E-CRNA-MM) AMS Author Profile; Scott, M. A. (1-BYU-CEV) AMS Author Profile; Tew, K. (1-BYU-IT) AMS Author Profile; Hughes, T. J. R. (1-TX-CPE) AMS Author Profile; Gomez, H. (1-PURD-SME) AMS Author Profile
Source
Subject
65 Numerical analysis -- 65D Numerical approximation and computational geometry
65D07Splines
74Mechanics of deformable solids -- 74L Special subfields of solid mechanics
74L15Biomechanical solid mechanics
65D07
74
74L15
Language
English
ISSN
18792138
Abstract
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.''