Deformable capsules can be used to model biological cells such as red blood cells. Developing fast and reliable numerical methods for simulation of capsules in pipe-confined flows is important in the construction of microfluidic devices for detection or analysis, e.g. in connection with medical screening. Such simulations can also be used to study capillary blood flow in the human body. We present a framework for fast and reliable simulation of capsules in unconfined or pipe-confined flow in three dimensions. Due to the small length scale, the flow is governed by the Stokes equations, which can be solved using a boundary integral method. This means that only the boundaries of the problem, i.e., the capsule membrane and pipe surface, need to be discretized. We use a Lagrangian discretization of the capsule membrane based on a partition of unity [Agarwal & Biros, 2024]. The interfacial force is computed from the local deformation gradient, and an explicit Runge–Kutta time-stepper is used to evolve the capsule. It is well known that capsule simulations are challenging, especially for long time horizons, due to numerical instabilities. These are due to e.g. CFL-like time-step restrictions, aliasing errors, and capsules developing features that are hard to resolve without aggressive local refinement. Our stability analysis for a spherical capsule based on [Veerapaneni et al., 2011] suggests that the underlying continuous problem is indeed stable. In this work, we combat the numerical instabilities by introducing a spectral filtering procedure that effectively acts as a low-pass filter on the capsule shape, removing high-frequency oscillations. We show that this permits stable long time simulations, and that the error introduced by filtering goes to zero with increasing resolution. The dense interactions between grid points are computed using a fast Ewald summation method [Bagge & Tornberg, 2023] in O(N log N) time for N grid points, which has been implemented both for CPU and GPU. A point of interest is to characterize the long-term dynamics of the capsule under different flow, material and geometric parameters, for which speed and stability are crucial. Especially the lateral drift of capsules is important in microfluidic sorting or filtering devices, and we will include such results in our presentation.