Biorthogonal Rosenbrock-Krylov time discretization methods
نویسندگان
چکیده
منابع مشابه
Exponential Rosenbrock-Type Methods
We introduce a new class of exponential integrators for the numerical integration of large-scale systems of stiff differential equations. These so-called Rosenbrock-type methods linearize the flow in each time step and make use of the matrix exponential and related functions of the Jacobian. In contrast to standard integrators, the methods are fully explicit and do not require the numerical sol...
متن کاملParallel exponential Rosenbrock methods
Exponential Rosenbrock integrators have been shown to be very efficient in solving large stiff differential systems of ODEs. So far, such exponential methods have been derived up to order 5. In this talk we give a convergence result for methods of order up to 6 and construct new integrators of orders 4, 5, and 6. In contrast to the existing schemes of orders 4 and 5, the new schemes, which are ...
متن کاملGlobalization strategies for Newton-Krylov methods for stabilized FEM discretization of Navier-Stokes equations
In this work we study the numerical solution of nonlinear systems arising from stabilized FEM discretizations of Navier–Stokes equations. This is a very challenging problem and often inexact Newton solvers present severe difficulties to converge. Then, they must be wrapped into a globalization strategy. We consider the classical backtracking procedure, a subspace trust-region strategy and an hy...
متن کاملPerturbation results for exponential Rosenbrock-type methods
In this note we consider exponential Rosenbrock-type methods that have been introduced in [1, 2, 3]. Since these methods involve several terms, which can not be computed exactly in praxis it is interesting to understand, how additional errors in the method affect the overall accuracy of the scheme. We will give a perturbation result for general perturbations and study the effect of inexact eval...
متن کاملEfficient Implicit Time-Marching Methods Using a Newton-Krylov Algorithm
The numerical behavior of two implicit time-marching methods is investigated in solving two-dimensional unsteady compressible flows. The two methods are the second-order multistep backward differencing formula and the fourth-order multistage explicit first stage, single-diagonal coefficient, diagonally implicit Runge-Kutta scheme. A Newton-Krylov method is used to solve the nonlinear problem ar...
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: Applied Numerical Mathematics
سال: 2020
ISSN: 0168-9274
DOI: 10.1016/j.apnum.2019.09.003