Improving Accuracy and Conditioning of Stokeslet Methods via Decoupled Force and Boundary Discretization

We introduce a decoupled submerged Stokeslet formulation for rigid-body Stokes flow in which the number of force points n is allowed to differ from the number of boundary collocation points N. Unlike the conventional Method of Fundamental Solutions (MFS), where the numbers of discretization points coincide, the present approach allows fewer force unknowns (n < N) and determines them in a least-squares sense. This structural decoupling acts as a discretization-level regularization, reducing condition numbers and suppressing non-physical force oscillations without modifying the Stokeslet kernel. Systematic benchmarks on spheres, spheroids, and asymmetric geometries show that moderate force reduction combined with appropriate submerging depth yields stable second- to third-order convergence. Compared with both conventional MFS and the Method of Regularized Stokeslets (MRS), the proposed formulation achieves improved conditioning and comparable or higher accuracy for a given boundary resolution, while retaining the simplicity of global Stokeslet representations.