Pseudo Time Continuation and Time Marching Methods for Monge-ampère Type Equations
نویسندگان
چکیده
We discuss the performance of three numerical methods for the fully nonlinear Monge-Ampère equation. The first two are pseudo time continuation methods while the third is a pure pseudo time marching algorithm. The pseudo time continuation methods are shown to converge for smooth data on a uniformly convex domain. We give numerical evidence that they perform well for the nondegenerate Monge-Ampère equation. The pseudo time marching method applies in principle to any nonlinear equation. Numerical results with this approach for the degenerate Monge-Ampère equation are given as well as for the Pucci and Gausscurvature equations.
منابع مشابه
Pseudo transient continuation and time marching methods for Monge-Ampère type equations
We present two numerical methods for the fully nonlinear elliptic MongeAmpère equation. The first is a pseudo transient continuation method and the second is a pure pseudo time marching method. The methods are proved to converge for smooth solutions. We give numerical evidence that they are also able to capture the viscosity solution of the Monge-Ampère equation. Even in the case of the degener...
متن کاملCalibrations Associated to Monge-ampère Equations
We show the volume maximizing property of the special Lagrangian submanifolds of a pseudo-Euclidean space. These special Lagrangian submanifolds arise locally as gradient graphs of solutions to MongeAmpère equations.
متن کاملDirichlet Problems of Monge-ampère Equations
This note presents a detailed and self-contained discussion of the Dirichlet problem of real Monge-Ampère equations in strictly convex domains and complex Monge-Ampère equations in strongly pseudo-convex domains. Sections 1.1 and 1.2 follow [2] and [3] respectively, while Sections 2.1, 2.2 and 2.3 are based on [5], [4] and [1] respectively. This note is written for lectures in the Special Lectu...
متن کاملOn the Integrability of a Class of Monge-Ampère Equations
We give the Lax representations for for the elliptic, hyperbolic and homogeneous second order Monge-Ampère equations. The connection between these equations and the equations of hydrodynamical type give us a scalar dispersionless Lax representation. A matrix dispersive Lax representation follows from the correspondence between sigma models, a two parameter equation for minimal surfaces and Mong...
متن کاملThe Monge-ampère Equation and Its Link to Optimal Transportation
We survey old and new regularity theory for the Monge-Ampère equation, show its connection to optimal transportation, and describe the regularity properties of a general class of Monge-Ampère type equations arising in that context.
متن کامل