Sparsifying preconditioner for soliton calculations
نویسندگان
چکیده
منابع مشابه
Sparsifying preconditioner for soliton calculations
We develop a robust and efficient method for soliton calculations for nonlinear Schrödinger equations. The method is based on the recently developed sparsifying preconditioner combined with Newton’s iterative method. The performance of the method is demonstrated by numerical examples of gap solitons in the context of nonlinear optics.
متن کاملSparsifying Preconditioner for the Lippmann-Schwinger Equation
The Lippmann–Schwinger equation is an integral equation formulation for acoustic and electromagnetic scattering from an inhomogeneous medium and quantum scattering from a localized potential. We present the sparsifying preconditioner for accelerating the iterative solution of the Lippmann–Schwinger equation. This new preconditioner transforms the discretized Lippmann–Schwinger equation into spa...
متن کاملSparsifying Preconditioner for Pseudospectral Approximations of Indefinite Systems on Periodic Structures
This paper introduces the sparsifying preconditioner for the pseudospectral approximation of highly indefinite systems on periodic structures, which include the frequency-domain response problems of the Helmholtz equation and the Schrödinger equation as examples. This approach transforms the dense system of the pseudospectral discretization approximately into a sparse system via an equivalent i...
متن کاملCombining Fast Multipole Techniques and an Approximate Inverse Preconditioner for Large Electromagnetism Calculations
The boundary element method has become a popular tool for the solution of Maxwell’s equations in electromagnetism. From a linear algebra point of view, this leads to the solution of large dense complex linear systems where the unknowns are associated with the edges of the mesh defined on the surface of the illuminated object. In this paper, we address the iterative solution of these linear syst...
متن کاملAdaptive Sparsifying Transforms for Iterative Tomographic Reconstruction
A major challenge in computed tomography imaging is to obtain high-quality images from low-dose measurements. Key to this goal are computationally efficient reconstruction algorithms combined with detailed signal models. We show that the recently introduced adaptive sparsifying transform (AST) signal model provides superior reconstructions from low-dose data at significantly lower cost than com...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2016
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2016.03.061