title: Adaptive step ODE algorithms for the 3D simulation of electric heart activity with graphics processing units.
abstract: In this paper we studied the implementation and performance of adaptive step methods for large systems of ordinary differential equations systems in graphics processing units, focusing on the simulation of three-dimensional electric cardiac activity. The Rush-Larsen method was applied in all the implemented solvers to improve efficiency. We compared the adaptive methods with the fixed step methods, and we found that the fixed step methods can be faster while the adaptive step methods are better in terms of accuracy and robustness.
authors.affiliation: Department of Information Systems and Computing, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain. Electronic address: vmgarcia@dsic.upv.es.
authors.forename: V M
authors.initials: VM
authors.lastname: Garcia-Molla
authors.affiliation: ITACA Institute, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain. Electronic address: allimas1987@gmail.com.
authors.forename: A
authors.initials: A
authors.lastname: Liberos
authors.affiliation: Department of Information Systems and Computing, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain. Electronic address: avidal@dsic.upv.es.
authors.forename: A
authors.initials: A
authors.lastname: Vidal
authors.affiliation: ITACA Institute, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain. Electronic address: mariaguillem@gmail.com.
authors.forename: M S
authors.initials: MS
authors.lastname: Guillem
authors.affiliation: ITACA Institute, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain. Electronic address: jmillet@eln.upv.es.
authors.forename: J
authors.initials: J
authors.lastname: Millet
authors.affiliation: ITEAM Institute, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain. Electronic address: agonzal@dcom.upv.es.
authors.forename: A
authors.initials: A
authors.lastname: Gonzalez
authors.affiliation: ITEAM Institute, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain. Electronic address: fjmartin@dcom.upv.es.
authors.forename: F J
authors.initials: FJ
authors.lastname: Martinez-Zaldivar
authors.affiliation: ITACA Institute, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain. Electronic address: acliment@itaca.upv.es.
authors.forename: A M
authors.initials: AM
authors.lastname: Climent
mesh_terms: D000465:Algorithms; D022062:Electrophysiologic Techniques, Cardiac / Q000379:methods*; D055724:Electrophysiological Phenomena; D006321:Heart; D006801:Humans; D008955:Models, Cardiovascular
keywords: Adaptive ODE solvers; Cardiac electrophysiology; Embedded Runge–Kutta methods; GPU computing; Rush–Larsen method