Finite Element Based Solution of Laplace's Equation Applied to Electrical Activity of the Human Body

Computer models are used in the study of electrocardiography to provide insight into physiological phenomena that are difficult to measure in the lab or in a clinical environment. <br />The electrocardiogram is an important tool for the clinician in that it changes characteristically in a numb...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autor principal:	Zainab T. Baqer
Formato:	article
Lenguaje:	EN
Publicado:	Al-Khwarizmi College of Engineering – University of Baghdad 2010
Materias:	Finite element ECG PCG volume conductor and GE. Chemical engineering TP155-156 Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/c7b31819746b4119b45d1ec1a7593fda
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:c7b31819746b4119b45d1ec1a7593fda
record_format	dspace
spelling	oai:doaj.org-article:c7b31819746b4119b45d1ec1a7593fda2021-12-02T01:52:26ZFinite Element Based Solution of Laplace's Equation Applied to Electrical Activity of the Human Body1818-1171https://doaj.org/article/c7b31819746b4119b45d1ec1a7593fda2010-01-01T00:00:00Zhttp://www.iasj.net/iasj?func=fulltext&aId=2191https://doaj.org/toc/1818-1171Computer models are used in the study of electrocardiography to provide insight into physiological phenomena that are difficult to measure in the lab or in a clinical environment. <br />The electrocardiogram is an important tool for the clinician in that it changes characteristically in a number of pathological conditions. Many illnesses can be detected by this measurement. By simulating the electrical activity of the heart one obtains a quantitative relationship between the electrocardiogram and different anomalies. <br />Because of the inhomogeneous fibrous structure of the heart and the irregular geometries of the body, finite element method is used for studying the electrical properties of the heart. <br />This work describes the implementation of the Conjugate Gradient iterative method for the solution of large linear equation systems resulting from the finite element method. A diagonal Jacobi preconditioner is used in order to accelerate the convergence. Gaussian elimination is also implemented and compared with the Precondition Conjugate Gradient (PCG) method and with the iterative method. Different types of matrix storage schemes are implemented such as the Compressed Sparse Row (CSR) to achieve better performance. In order to demonstrate the validity of the finite element analysis, the technique is adopted to solve Laplace's equation that describes the electrical activity of the human body with Dirichlet and Neumann boundary conditions. An automatic mesh generator is built using C++ programming language. Initially a complete finite element program is built to solve Laplace's equation. The same accuracy is obtained using these methods. The results show that the CSR format reduces computation time compared to the order format. The PCG method is better for the solution of large linear system (sparse matrices) than the Gaussian Elimination and back substitution method, while Gaussian elimination is better than iterative method. <br />Zainab T. BaqerAl-Khwarizmi College of Engineering – University of BaghdadarticleFinite elementECGPCGvolume conductor and GE.Chemical engineeringTP155-156Engineering (General). Civil engineering (General)TA1-2040ENAl-Khawarizmi Engineering Journal, Vol 6, Iss 4, Pp 37-51 (2010)
institution	DOAJ
collection	DOAJ
language	EN
topic	Finite element ECG PCG volume conductor and GE. Chemical engineering TP155-156 Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	Finite element ECG PCG volume conductor and GE. Chemical engineering TP155-156 Engineering (General). Civil engineering (General) TA1-2040 Zainab T. Baqer Finite Element Based Solution of Laplace's Equation Applied to Electrical Activity of the Human Body
description	Computer models are used in the study of electrocardiography to provide insight into physiological phenomena that are difficult to measure in the lab or in a clinical environment. <br />The electrocardiogram is an important tool for the clinician in that it changes characteristically in a number of pathological conditions. Many illnesses can be detected by this measurement. By simulating the electrical activity of the heart one obtains a quantitative relationship between the electrocardiogram and different anomalies. <br />Because of the inhomogeneous fibrous structure of the heart and the irregular geometries of the body, finite element method is used for studying the electrical properties of the heart. <br />This work describes the implementation of the Conjugate Gradient iterative method for the solution of large linear equation systems resulting from the finite element method. A diagonal Jacobi preconditioner is used in order to accelerate the convergence. Gaussian elimination is also implemented and compared with the Precondition Conjugate Gradient (PCG) method and with the iterative method. Different types of matrix storage schemes are implemented such as the Compressed Sparse Row (CSR) to achieve better performance. In order to demonstrate the validity of the finite element analysis, the technique is adopted to solve Laplace's equation that describes the electrical activity of the human body with Dirichlet and Neumann boundary conditions. An automatic mesh generator is built using C++ programming language. Initially a complete finite element program is built to solve Laplace's equation. The same accuracy is obtained using these methods. The results show that the CSR format reduces computation time compared to the order format. The PCG method is better for the solution of large linear system (sparse matrices) than the Gaussian Elimination and back substitution method, while Gaussian elimination is better than iterative method. <br />
format	article
author	Zainab T. Baqer
author_facet	Zainab T. Baqer
author_sort	Zainab T. Baqer
title	Finite Element Based Solution of Laplace's Equation Applied to Electrical Activity of the Human Body
title_short	Finite Element Based Solution of Laplace's Equation Applied to Electrical Activity of the Human Body
title_full	Finite Element Based Solution of Laplace's Equation Applied to Electrical Activity of the Human Body
title_fullStr	Finite Element Based Solution of Laplace's Equation Applied to Electrical Activity of the Human Body
title_full_unstemmed	Finite Element Based Solution of Laplace's Equation Applied to Electrical Activity of the Human Body
title_sort	finite element based solution of laplace's equation applied to electrical activity of the human body
publisher	Al-Khwarizmi College of Engineering – University of Baghdad
publishDate	2010
url	https://doaj.org/article/c7b31819746b4119b45d1ec1a7593fda
work_keys_str_mv	AT zainabtbaqer finiteelementbasedsolutionoflaplacesequationappliedtoelectricalactivityofthehumanbody
_version_	1718402865693720576

Finite Element Based Solution of Laplace's Equation Applied to Electrical Activity of the Human Body

Ejemplares similares