Image Processing & Communication, vol. 17, no. 4, pp. 339-346 DOI: 10.2478/v10248-012-0063-6 339 APPLICATION OF GPU PARALLEL COMPUTING FOR ACCELERATION OF FINITE ELEMENT METHOD BASED 3D RECONSTRUCTION ALGORITHMS IN ELECTRICAL CAPACITANCE TOMOGRAPHY PAWEL KAPUSTA,MICHAL MAJCHROWICZ,DOMINIK SANKOWSKI ,ROBERT BANASIAK Institute of Applied Computer Science, Lodz University of Technology, Poland pkapust.kis.p.lodz.pl Abstract. With the increasing complexity and scale of industrial processes their visualization is becoming increasingly important. Especially popular are non-invasive methods, which do not interfere directly with the process. One of them is the 3D Electrical Capacitance Tomography. It possesses however a serious flaw - in order to obtain a fast and accurate visualization requires application of computationally intensive algo- rithms. Especially non-linear reconstruction using Finite Element Method is a multistage, complex numerical task, requiring many lin- ear algebra transformations on very large data sets. Such process, using traditional CPUs can take, depending on the used meshes, up to sev- eral hours. Consequently it is necessary to de- velop new solutions utilizing GPGPU (General Purpose Computations on Graphics Processing Units) techniques to accelerate the reconstruc- tion algorithm. With the developed hybrid par- allel computing architecture, based on sparse matrices, it is possible to perform tomographic calculations much faster using GPU and CPU simultaneously, both with Nvidia CUDA and OpenCL. 1 Introduction Increasingly important is the need for automated, real- time monitoring and diagnosing of industrial processes, towards a better understanding of the phenomena occur- ring in them and to prevent potential accidents and disas- ters. In this field a number of, rapidly developing new non-invasive measurement methods of tomographic na- ture exist. These techniques are gaining in popularity es- pecially as they provide effective tools for the visualiza- tion without interfering in the process. From the process diagnosis and monitoring point of view the existing non-invasive imaging methods can be divided into two families: static and dynamic tomography of cross-section (2D) [5], and static and dynamic three- dimensional tomography of volume (3D/4D) [1, 2, 3, 4]. The first family uses variety of data processing and visu- alization algorithms that are able to process the measure- ment data in real time using currently available computa- tional power of processors. This group, having a three- dimensional nature, often requires processing of much