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

适用于材料科学和工程应用的快速收敛、高性能 PDE 求解器：理论、实现和应用。

• 批准号: 1008631
• 负责人: Oscar Bruno
• 金额: $ 55万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-15 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1008631&HistoricalAwards=false
• 关键词: Rapidly; convergent; performance; PDE; solvers

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.

BrunoDMS-1008631 研究人员开发并分析了新颖的高性能、高精度数值算法，用于计算偏微分方程 (PDE) 的解，并应用于材料科学、工程和医学领域的广泛问题。 PDE 求解器适用于涉及以下问题： (i) 内部和周围的各种物理可观测值（弹性和电磁场、线性和非线性声场、热场、流体流动） (ii) 复杂结构（光子或电子设备、带有角、边缘或裂缝的奇异几何形状、解剖几何形状、金属或现代建造的空气、水或陆地车辆） 复合材料），并含有（iii）流体或固体材料——包括复合弹性介质、电介质、完美和有损导体、可压缩和不可压缩流体，以及导致色散和频率相关吸收的介质。拟议工作的计算方法基于近年来在研究者的指导下开发的一类数值求解器以及表面表示和网格划分方法。 这些是基于傅里叶的积分和微分求解器，可以为现实的工程几何形状生成具有高阶精度、无条件稳定性和无数值色散的解决方案，包括完整的飞机、医疗应用的复杂解剖结构、复杂的光子或电子设备等特征。 在实践中，在给定的精度下，这些类型的求解器的数值计算速度比其他一些最具竞争力的求解器快数千倍：新方法可以解决以前棘手的问题。 该项目影响多个社会领域，包括医学（诊断和治疗超声，应用于肿瘤检测、肾结石破坏和靶向药物输送）、电气工程（光学、电子）、军事和民用遥感和通信（雷达、声纳、隐形、天线）、高效空中、水上或陆地车辆的设计等。 新算法在许多具有挑战性的案例研究中显示出比以前的方法快一千倍的速度，可以解决上述领域中以前棘手的问题。 该项目还培训研究生和本科生以及博士后。 例如，本科生在一个综合环境中开展整个夏季的研究项目，其中包括研究生和博士后、研究者以及提出具体工程问题的一些工业和实验室研究人员。