TwoCircularMethoden

TwoCircularMethoden is a term used in numerical analysis and computational physics to describe a pair of iterative solvers designed for problems defined on circular or radially symmetric domains. The term appears in some German-language literature that blends English and German terminology. The core idea is to exploit circular symmetry by decomposing the problem into radial and angular components and to apply two complementary update rules in succession until convergence.

The two methods are typically designated as the first circular method and the second circular method. The first method updates the solution by solving a radial subproblem while keeping angular modes fixed, and the second method updates by solving an angular subproblem with radial modes fixed. In practice, the methods are implemented as alternating sweeps that transfer information between radial and angular representations, or as two operators that act on the same discrete grid with different boundary-handling strategies.

Convergence properties depend on the problem class, such as elliptic partial differential equations or integral equations, and on the discretization. Under suitable conditions, the iteration operator has a spectral radius less than one, yielding linear convergence; acceleration can be achieved by relaxation, over-relaxation, or Krylov-accelerated variants.

Applications include electromagnetics, acoustics, heat conduction on circular domains, and image or signal processing tasks that benefit from circular symmetry. The term is not universally standardized, and exact definitions may vary across sources. Readers should check the specific context in which TwoCircularMethoden is used.