Fluid-structure interaction is studied numerically in academics and the industry. Shear computational power alone is insufficient to accurately resolve the complex dynamics of high Reynolds number fluid flow. Therefore the development of more efficient and applicable computational algorithms is important. This dissertation focuses on the use of vortex particle methods and computational efficiency. The work is divided into three parts. A novel method for the simulation of the aerodynamic admittance in bluff body aerodynamics is presented. The method involves a model for describing oncoming turbulence in two-dimensional discrete vortex method simulations by seeding the upstream flow with vortex particles. The turbulence is generated prior to the simulations and is based on analytic spectral densities of the atmospheric turbulence and a coherence function defining the spatial correlation of the flow. The method is validated by simulating the turbulent flow past a flat plate and past the Great Belt East bridge, the Øresund bridge and the Busan-Geoje bridge. The dissertation introduces a novel multiresolution vortex-in-cell algorithm using patches of varying resolution. The Poisson equation relating the fluid vorticity and velocity is solved using fast Fourier transforms subject to free-space boundary conditions. Solid boundaries are implemented using the semi-implicit formulation of Brinkman penalization and it is shown that the penalization can be carried out as a simple interpolation. The implementation is two-dimensional and sequential. The implementation is validated against the analytic solution to the Perlman test case and by free-space simulations of the onset flow around fixed and rotating circular cylinders and bluff body flows around bridge sections. Finally a three-dimensional vortex-in-cell algorithm is implemented into an existing open source library that enables large scale, three-dimensional particle-vortex simulations. A high order Fourier based Poisson solver is presented using novel use of regularization in the vortex-in-cell algorithm which formally enables arbitrarily high order convergence. The implementation is prepared for multiresolution though it is currently not supported by the parallel framework. The simulation of deformable and moving objects is demonstrated using Brinkman penalization and the vortex-in-cell algorithm. The model is applied to flow around spheres, a bridge section during the construction phase and the swimming motion of the medusa Aurelia aurita.