Deformable objects such as drops, vesicles and red blood cells have received considerable research interest due to their industrial and biomedical applications. For example, the study of the deformation of drops is important to investigate the dynamics of polymer blends intended for fiber-, film- or bulk polymer production or water-in-water biopolymer mixtures. Capsules, vesicles and red blood cells (RBC) also play an essential role in biomedical engineering. To obtain a useful model for the motion of these objects, an accurate and powerful method to approximate the velocity field of the deformable objects is required. The boundary integral method (BIM), which relies on a mathematical reduction from the three-dimensional volume description to a two-dimensional surface representation, is one of the most accurate known methods to approximate this velocity field in the creeping flow regime and is used in this thesis.

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