Adjoint equation
Encyclopedia
An adjoint equation is a linear differential equation
, usually derived from its primal equation using integration by parts
. Gradient values with respect to a particular quantity of interest can be efficiently calculated by solving the adjoint equation. Methods based on solution of adjoint equations are used in wing shape optimization
, fluid flow control and uncertainty quantification
.
Linear differential equation
Linear differential equations are of the formwhere the differential operator L is a linear operator, y is the unknown function , and the right hand side ƒ is a given function of the same nature as y...
, usually derived from its primal equation using integration by parts
Integration by parts
In calculus, and more generally in mathematical analysis, integration by parts is a rule that transforms the integral of products of functions into other integrals...
. Gradient values with respect to a particular quantity of interest can be efficiently calculated by solving the adjoint equation. Methods based on solution of adjoint equations are used in wing shape optimization
Wing shape optimization
Wing-shape optimization is a software implementation of shape optimization primarily used for aircraft design. This allows for engineers to produce more efficient and cheaper aircraft designs.-History:...
, fluid flow control and uncertainty quantification
Uncertainty quantification
Uncertainty quantification is the science of quantitative characterization and reduction of uncertainties in applications. It tries to determine how likely certain outcomes are if some aspects of the system are not exactly known...
.