Mathematics and Engineering Analysis
M&CT's Mathematics and Engineering Analysis unit is Boeing's central math resource -- about 100 mathematicians and scientists with extensive experience in industrial R&D and problem solving. The organization's experts are skilled in applied statistics, computational science, computational linear algebra and differential equations, geometry and optimization, mathematical modeling, operations research, and modeling and simulations technology. They work with engineers and other technologists on the design and manufacturing of commercial airplanes and military and space systems. They also conduct applied R&D and do consulting and software development for non-Boeing customers.
Applied Statistics
The Applied Statistics group is devoted to a combination of R&D and consulting in support of aerospace industry needs. Their work ranges through most standard areas of industrial statistics: survey design and analysis, time series and forecasting, probability and stochastic models, statistical quality control, Design of Experiments (DOE), and reliability.
The aerospace industry, rich in diverse and complex problems, has led us to other areas including image processing, spatial statistics, industrial epidemiology, data mining, design and analysis of computer experiments, Bayesian information retrieval, financial modeling, stochastic optimization, and statistical tolerancing.
Computational Science
The Computational Science group provides software and support to Boeing engineers and mathematicians engaged in solving the mathematical problems that arise while using computers to design complex structures and aircraft and simulate airflow.
The group's areas of expertise include:
- Application of parallel computing techniques to mathematical computation
- Web-enabled delivery and analysis tools
- Advanced engineering computing techniques
- C, C++, Fortran, Java, and Visual Basic programming languages
- Mathematical software
Computational Linear Algebra and Differential Equations
The Computational Linear Algebra and Differential Equations group works with Boeing engineers to develop efficient solutions for computer-aided design problems in these and other areas:
- Computational fluid dynamics
- Electromagnetics, radar cross sections
- Electrical systems analysis
- Large sparse linear systems and least squares solutions
- Partial and ordinary differential equations
- Integral equations
- Iterative methods
- Computational physics
The level of detail in modern designs can demand the solution of systems of linear equations involving as many as one trillion variables. The Computational Linear Algebra and Differential Equations group works to develop algorithms that solve such problems in a reasonable amount of time on advanced computing architectures.
Geometry and Optimization
Geometry and Optimization is a group of specialists in geometric modeling, optimization, design methods, data fitting, computational geometry and optimal control. The Geometry and Optimization group focuses on the following technology areas.
Design space exploration and multidisciplinary design optimization:
- Design Explorer software
- Multidisciplinary design optimization
- Surrogate modeling and response surfaces
- Global optimization methods and software
- Multi-objective optimization
Geometric modeling and computer-aided geometric design:
- General Geometry Generator (parametric geometry creation)
- Geometric methods and algorithms
- Analysis and "repair" of curves and surfaces
- Geometry software libraries
Numerical optimization and optimal control:
- Sparse optimal control software (SOCS)
- Very large scale optimization
- Nonlinear programming
Mathematical Modeling
The Mathematical Modeling group creates predictive models and analyses that lead to understanding and better design. Their work is centered on the following technology areas.
Physics-based modeling:
- New approaches for autonomous damage evolution -- multi-crack and unguided crack path evolution
- Very large strain (friction stir welding) modeling
- Structural response to multi-mode loading and dynamics
- Math for process design and analysis-- tape laying path planning, machining, drilling, forming, and peening
Continuous function data fusion:
- Nondestructive testing and evaluation
- Subpixel deconvolution algorithms
- Very fast, functional, implicit geometry representation applications
Operations Research
The Operations Research group develops and applies scientific methods for decision making, optimal planning, scheduling, and resource allocation. Some of the focus areas for the group include the following:
- Resource allocation and planning
- Sequencing and assignment
- Routing and scheduling
- Inventory management
- Modeling and simulation
- Mathematical programming
- Optimization
Modeling and Simulation Technology
The Modeling and Simulation Technology group focuses on the following technology areas:
- Distributed modeling and simulation architecture and tools
- Modeling and simulation supporting system verification and analysis
- Modeling and simulation processes
- Simulation-based acquisition support
- Modeling and simulation standards
- High-risk modeling and simulation development