# Applications of linear algebra in the design of aircraft [closed]

David Lay mentioned one application of linear algebra in the design of aircraft in the introductory part of chapter 2 of his book:

[...] A computer creates a model of the surface by first superimposing a three-dimensional grid of “boxes” on the original wire-frame model. Boxes in this grid lie either completely inside or completely outside the plane, or they intersect the surface of the plane. The computer selects the boxes that intersect the surface and subdivides them, retaining only the smaller boxes that still intersect the surface. The subdividing process is repeated until the grid is extremely fine. A typical grid can include more than 400,000 boxes. The process for finding the airflow around the plane involves repeatedly solving a system of linear equations $$Ax=b$$ that may involve up to 2 million equations and variables. The vector $$b$$ changes each time, based on data from the grid and solutions of previous equations.

Where can I find details about the boldfaced part? Can someone briefly give the general idea?

• – Piyush Grover Jan 30 '20 at 14:36
• a Google search for "finite element aircraft design" should give you a good set of pointers; for a useful MO question you would want to focus on a particular advanced math issue, I think. – Carlo Beenakker Jan 31 '20 at 9:01