Schwinn, ChristianChristianSchwinnGörlitz, AndreasAndreasGörlitzHildenbrand, DietmarDietmarHildenbrand2022-03-112022-03-112009https://publica.fraunhofer.de/handle/publica/364725Geometric Algebra (GA) is a mathematical framework that allows a compact, geometrically intuitive description of geometric relationships and algorithms. These algorithms require significant computational power because of the intrinsically high dimensionality of geometric algebras. Algorithms in an n-dimensional GA require 2n elements to be computed for each multivector. GA is not restricted to a maximum of dimensions, so arbitrary geometric algebras can be constructed over a vector space Vn. Since computations in GA can be highly parallelized, the benefits of a parallel computing architecture can lead to a significant speed-up compared to standard CPU implementations, where elements of the algebra have to be calculated sequentially. An upcoming approach of coping with parallel computing is to use general-purpose computation on graphics processing units (GPGPU). In this paper, we focus on the Compute Unified Device Architecture (CUDA) from NVIDIA [9]. We present a code generator that takes as input the description of an arbitrary geometric algebra and produces an implementation of geometric products for the underlying algebra on the CUDA platform.engeometric algebrageometric computingGraphics Processing Unit (GPU)Compute Unified Device Architecture (CUDA)Forschungsgruppe Geometric Algebra Computing (GACO)006conference paper