# Efficient Exponential Integrator Finite Element Method for Semilinear Parabolic Equations

@article{Huang2022EfficientEI, title={Efficient Exponential Integrator Finite Element Method for Semilinear Parabolic Equations}, author={Jianguo Huang and Lili Ju and Yu Tang Xu}, journal={ArXiv}, year={2022}, volume={abs/2209.11922} }

In this paper, we propose an e ﬃ cient exponential integrator ﬁnite element method for solving a class of semilinear parabolic equations in rectangular domains. The proposed method ﬁrst performs the spatial discretization of the model equation using the ﬁnite element approximation with continuous multilinear rectangular basis functions, and then takes the explicit exponential Runge-Kutta approach for time integration of the resulting semi-discrete system to produce fully-discrete numerical…

## References

SHOWING 1-10 OF 45 REFERENCES

### A fast compact exponential time differencing method for semilinear parabolic equations with Neumann boundary conditions

- MathematicsAppl. Math. Lett.
- 2019

### Fast Explicit Integration Factor Methods for Semilinear Parabolic Equations

- MathematicsJ. Sci. Comput.
- 2015

In this paper, an explicit numerical method and its fast implementation are proposed and discussed for the solution of a wide class of semilinear parabolic equations including the Allen–Cahn equation…

### Overlapping domain decomposition based exponential time differencing methods for semilinear parabolic equations

- Mathematics, Computer ScienceBIT Numerical Mathematics
- 2020

This paper focuses on numerical solutions of a class of semilinear parabolic equations with the well-known Allen–Cahn equation as a special case and proves the convergence of the fully discrete localized solutions to the exact semi-discrete solution and the converge of the iterative solutions.

### A fast compact time integrator method for a family of general order semilinear evolution equations

- Mathematics, Computer ScienceJ. Comput. Phys.
- 2019

### Fast High-Order Compact Exponential Time Differencing Runge–Kutta Methods for Second-Order Semilinear Parabolic Equations

- Mathematics, Computer ScienceJ. Sci. Comput.
- 2016

The proposed methods are explicit in nature, and use exponential time differencing and Runge–Kutta approximations in combination with a linear splitting technique to achieve accurate and stable time integration of second-order semilinear parabolic equations in regular domains.

### Maximum bound principle preserving integrating factor Runge-Kutta methods for semilinear parabolic equations

- Computer Science, MathematicsJ. Comput. Phys.
- 2021

### Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems

- Mathematics, Computer ScienceSIAM J. Numer. Anal.
- 2005

The aim of this paper is to analyze explicit exponential Runge--Kutta methods for the time integration of semilinear parabolic problems in an abstract Banach space framework of sectorial operators and locally Lipschitz continuous nonlinearities and construct methods that do not suffer from order reduction.

### High-order solution of one-dimensional sine-Gordon equation using compact finite difference and DIRKN methods

- MathematicsMath. Comput. Model.
- 2010

### Explicit exponential Runge-Kutta methods of high order for parabolic problems

- Mathematics, Computer ScienceJ. Comput. Appl. Math.
- 2014

### Implicit-explicit methods for time-dependent partial differential equations

- Computer Science
- 1995

This work systematically analyze the performance of implicit-explicit IMEX schemes, propose improved new schemes, and pay particular attention to their relative performance in the context of fast multigrid algorithms and of aliasing reduction for spectral methods.