# On variational iterative methods for semilinear problems

## TL;DR

This paper introduces an iterative approach for semilinear problems that simplifies them into linear systems solvable by fast Poisson solvers, demonstrating efficiency and accuracy through theoretical analysis and experiments.

## Contribution

The paper proposes a novel iterative method that reduces semilinear problems to linear systems, enabling faster and accurate solutions compared to existing methods.

## Key findings

- Method reduces computational cost significantly.
- Achieves high accuracy in numerical approximations.
- Supported by theoretical analysis and experimental validation.

## Abstract

This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into linear systems which are solvable using fast Poisson solvers. Theoretical justifications are provided and supported by several experiments. Numerical results show that the method is not only computationally less expensive, but also yields accurate approximations.