Rapidly-convergent, high-performance PDE solvers for materials-science and engineering applications: theory, implementation and applications.

点击翻译按钮获取中文摘要

BrunoDMS-1008631 The investigator develops and analyzes novelhigh-performance, highly accurate numerical algorithms forcomputing solutions of partial differential equations (PDE), withapplication to a wide range of problems in materials science,engineering and medicine. The PDE solvers apply to problemsinvolving: (i) Various physical observables (elastic andelectromagnetic fields, linear and nonlinear acoustic fields,thermal fields, fluid-flow) within and around (ii) Complexstructures (photonic or electronic devices, singular geometrieswith corners, edges or cracks, anatomic geometries, air, water orland vehicles built from metals or modern composite materials),and containing (iii) Fluids or solid materials -- includingcomposite elastic media, dielectrics, perfect and lossyconductors, compressible and incompressible fluids, as well asmedia leading to dispersion and frequency-dependent absorption. The computational methodology underlying the proposed work isbased on a class of numerical solvers and surface-representationand meshing methodologies developed in recent years under thedirection of the investigator. These are Fourier-based integraland differential solvers that can produce solutions withhigh-order accuracy, unconditional stability, and no numericaldispersion, for realistic engineering geometries includingfeatures such as full aircraft, complex anatomic configurationsfor medical applications, complex photonic or electronic devices,etc. In practice, these types of solvers have demonstrated up toone-thousand times faster numerics, for a given accuracy, thansome of the most competitive solvers otherwise available: the newmethods can enable solution of previously intractable problems. The project impacts upon a variety of areas of societalinterest, including medicine (diagnostic and therapeuticultrasound with application to, e.g., tumor detection, kidneystone destruction, and targeted drug delivery), electricalengineering (optics, electronics), military and civilian remotesensing and communications (radar, sonar, stealth, antennas),design of efficient air, water or land vehicles, etc. The newalgorithms, which in a number of challenging case studies havedemonstrated up to one-thousand times faster numerics thanprevious approaches, enable solution of previously intractableproblems in areas such as those mentioned above. The projectalso trains graduate and undergraduate students and postdoctoralassociates. Undergraduate students, for example, carry outsummer-long research projects in an integrative environmentinvolving graduate students and postdocs as well as theinvestigator and some of the industrial and lab researchers whopropose specific engineering problems.