This report documents the program and the outcomes of Dagstuhl Seminar 17221 "Geometric Mode... more This report documents the program and the outcomes of Dagstuhl Seminar 17221 "Geometric Modelling, Interoperability and New Challenges". While previous Dagstuhl seminars on geometric modeling were focused on basic research, this seminar was focused on applications of geometric modeling to four topic areas: big data and cloud computing, multi-material additive manufacturing, isogeometric analysis, and design optimization. For this purpose we brought together participants from industry urgently in need of better solutions, researchers in the above application areas, and researchers in the geometric modeling community.
This chapter discusses Geometry Processing. Geometry processing focuses on those quantities that ... more This chapter discusses Geometry Processing. Geometry processing focuses on those quantities that can be derived solely from given geometry. The chapter discusses various examples of geometric analysis, including determination of extreme points of the geometry, intersections of geometrical components, and metric information, such as position, length, area, or volume. Most geometry processing can be accomplished through some combination of evaluation of functions, contouring, rootfinding, and numerical integration. The chapter describes rootfinding and numerical integration, and also discusses the way both can be used to create more sophisticated geometry processing techniques. Many geometric analyses require integration over curves and surfaces as a key component of the analysis. Such computations include length of curves, area of surfaces, center of gravity and moment of inertia of volumes, and mass of variable density media. Numerical integration focuses on some issues that arise when these methods are applied to problems in geometric modeling.
We describe Boeing’s Applied Mathematics organization, the work we do, and how it contributes to ... more We describe Boeing’s Applied Mathematics organization, the work we do, and how it contributes to Boeing’s business goals. We address some of the ICIAM goals relating to education and mathematics in industry, and we try to convey the challenge and satisfaction that come from applied mathematics in the aerospace business. We discuss the qualifications we look for in job candidates and how university mathematicians might learn more about industrial careers. After some examples from the Applied Math organization as a whole, we go into detail about multidisciplinary design optimization, the primary focus of the Geometry and Optimization group. We illustrate our methods with an example, the design of a hypersonic vehicle. Finally we discuss some of the non-technical challenges mathematicians in industry often face.
15th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, 2008
To achieve closure on the physical and economic performance metrics of air-breathing hypersonic v... more To achieve closure on the physical and economic performance metrics of air-breathing hypersonic vehicles, their components and functions must be highly integrated. Such extensive integration challenges conventional desig n paradigms, approaches and tools. Unconventional approaches must therefore be developed and employed to achieve design success, among them parametric configuration definition, automated engineering and highfidelity discipline analysis, and multidisciplinary optimization, to name a few. These and other advanced design technologies are being develo ped and applied at Boeing to the design of hypersonic vehicles, as well as to other Boeing aerospace platforms. This paper describes recent Boeing progress in developing and applying t he elements of a multidisciplinary analysis and optimization system to hypersonic vehi cle design, and outlines future work aimed at further developing this critical capabilit y.
After assigning Mariner season tickets in a rather unsatisfying way in 1996 to the individuals wh... more After assigning Mariner season tickets in a rather unsatisfying way in 1996 to the individuals who had agreed to buy and divide them, we devised a more sophisticated approach in 1997 that poses and solves a mixed-integer-programming problem, and we obtained much more satisfactory results.
This report documents the program and the outcomes of Dagstuhl Seminar 17221 "Geometric Mode... more This report documents the program and the outcomes of Dagstuhl Seminar 17221 "Geometric Modelling, Interoperability and New Challenges". While previous Dagstuhl seminars on geometric modeling were focused on basic research, this seminar was focused on applications of geometric modeling to four topic areas: big data and cloud computing, multi-material additive manufacturing, isogeometric analysis, and design optimization. For this purpose we brought together participants from industry urgently in need of better solutions, researchers in the above application areas, and researchers in the geometric modeling community.
This chapter discusses Geometry Processing. Geometry processing focuses on those quantities that ... more This chapter discusses Geometry Processing. Geometry processing focuses on those quantities that can be derived solely from given geometry. The chapter discusses various examples of geometric analysis, including determination of extreme points of the geometry, intersections of geometrical components, and metric information, such as position, length, area, or volume. Most geometry processing can be accomplished through some combination of evaluation of functions, contouring, rootfinding, and numerical integration. The chapter describes rootfinding and numerical integration, and also discusses the way both can be used to create more sophisticated geometry processing techniques. Many geometric analyses require integration over curves and surfaces as a key component of the analysis. Such computations include length of curves, area of surfaces, center of gravity and moment of inertia of volumes, and mass of variable density media. Numerical integration focuses on some issues that arise when these methods are applied to problems in geometric modeling.
We describe Boeing’s Applied Mathematics organization, the work we do, and how it contributes to ... more We describe Boeing’s Applied Mathematics organization, the work we do, and how it contributes to Boeing’s business goals. We address some of the ICIAM goals relating to education and mathematics in industry, and we try to convey the challenge and satisfaction that come from applied mathematics in the aerospace business. We discuss the qualifications we look for in job candidates and how university mathematicians might learn more about industrial careers. After some examples from the Applied Math organization as a whole, we go into detail about multidisciplinary design optimization, the primary focus of the Geometry and Optimization group. We illustrate our methods with an example, the design of a hypersonic vehicle. Finally we discuss some of the non-technical challenges mathematicians in industry often face.
15th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, 2008
To achieve closure on the physical and economic performance metrics of air-breathing hypersonic v... more To achieve closure on the physical and economic performance metrics of air-breathing hypersonic vehicles, their components and functions must be highly integrated. Such extensive integration challenges conventional desig n paradigms, approaches and tools. Unconventional approaches must therefore be developed and employed to achieve design success, among them parametric configuration definition, automated engineering and highfidelity discipline analysis, and multidisciplinary optimization, to name a few. These and other advanced design technologies are being develo ped and applied at Boeing to the design of hypersonic vehicles, as well as to other Boeing aerospace platforms. This paper describes recent Boeing progress in developing and applying t he elements of a multidisciplinary analysis and optimization system to hypersonic vehi cle design, and outlines future work aimed at further developing this critical capabilit y.
After assigning Mariner season tickets in a rather unsatisfying way in 1996 to the individuals wh... more After assigning Mariner season tickets in a rather unsatisfying way in 1996 to the individuals who had agreed to buy and divide them, we devised a more sophisticated approach in 1997 that poses and solves a mixed-integer-programming problem, and we obtained much more satisfactory results.
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