We compare different Poisson solvers within the context of an electrostatic Vlasov-Poisson system. These schemes are implemented as part of the IPPL (Independent Parallel Particle Layer) library (Frey et al., 2024), which provides performance portable and dimension independent building blocks for scientific simulations requiring particle-mesh methods, with Eulerian (mesh-based) and Lagrangian (particle-based) approaches. The simulation used to compare the performance and portability of the schemes is Landau damping, part of a set of mini-applications implemented to benchmark and showcase the capabilities of the IPPL library (Muralikrishnan et al., 2024). We use grid-sizes of $512^3$ and $1024^3$ with 8 particles per cell, running with different algorithms in the solve phase of the Particle-in-Cell (PIC) loop: a Fast Fourier Transform (FFT) pseudo-spectral solver, a matrix-free finite difference Preconditioned Conjugate Gradient (PCG) solver, and a matrix-free Finite Element (FEM) solver. We also compare these PIC schemes to the novel Particle-in-Fourier (PIF) scheme, which performs interpolations using non-uniform FFTs thereby avoiding a grid in the real space. We obtain results on different computing architectures, such as AMD GPUs (LUMI at CSC), and Nvidia GPUs (Alps at CSCS and JUWELS Booster at Jülich Supercomputing Center), showcasing portability. In terms of absolute time the FFT solver is advantageous, but is limited in its applicability. All other field solvers in the PIC scheme are an order-of-magnitude more expensive in terms of time, but scale similarly to the FFT case in the electrostatic PIC context. The PIF scheme serves as a high fidelity alternative to standard PIC, and while it is costlier than the FFT-based PIC scheme, it shows excellent scalability on all the architectures.

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