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Efficient simulation of cardiac electrical propagation using high order finite elements.

Arthurs CJ, Bishop MJ, Kay D - J Comput Phys (2012)

Bottom Line: We detail the hurdles which must be overcome in order to achieve theoretically-optimal errors in the approximations generated, including the choice of method for approximating the solution to the cardiac cell model component.We place our work on a solid theoretical foundation and show that it can greatly improve the accuracy in the approximation which can be achieved in a given amount of processor time.Our results demonstrate superior accuracy over linear finite elements at a cheaper computational cost and thus indicate the potential indispensability of our approach for large-scale cardiac simulation.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer Science, University of Oxford, Oxford, United Kingdom.

ABSTRACT
We present an application of high order hierarchical finite elements for the efficient approximation of solutions to the cardiac monodomain problem. We detail the hurdles which must be overcome in order to achieve theoretically-optimal errors in the approximations generated, including the choice of method for approximating the solution to the cardiac cell model component. We place our work on a solid theoretical foundation and show that it can greatly improve the accuracy in the approximation which can be achieved in a given amount of processor time. Our results demonstrate superior accuracy over linear finite elements at a cheaper computational cost and thus indicate the potential indispensability of our approach for large-scale cardiac simulation.

No MeSH data available.


Three of the ten hierarchical basis function piecesrequired in 2D on the reference element for a cubic finite element approximationof the solution. Note that when mapped to the real mesh from the referenceelement, each of these is just part of one of the basis functions that isactually supported on multiple elements.
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f0005: Three of the ten hierarchical basis function piecesrequired in 2D on the reference element for a cubic finite element approximationof the solution. Note that when mapped to the real mesh from the referenceelement, each of these is just part of one of the basis functions that isactually supported on multiple elements.

Mentions: We take the hierarchical approach because it has theadvantage that on each element the basis of degree pis the same as the basis of degree p + 1 with the degree p + 1 functions removed. This lends itself toadaptive techniques, although we do not explore them here. For example, withp = 3 on a 1Dreference element [0, 1] we havex,1-x,x(1-x)andx(1-x)12-xwhich are the two components of a linear basis function, thequadratic and the cubic respectively. In 2D the analogous approach has threelinear, three quadratic and four cubic basis functions partially or whollysupported on each element; see Fig.1 for some ofthese.


Efficient simulation of cardiac electrical propagation using high order finite elements.

Arthurs CJ, Bishop MJ, Kay D - J Comput Phys (2012)

Three of the ten hierarchical basis function piecesrequired in 2D on the reference element for a cubic finite element approximationof the solution. Note that when mapped to the real mesh from the referenceelement, each of these is just part of one of the basis functions that isactually supported on multiple elements.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4067136&req=5

f0005: Three of the ten hierarchical basis function piecesrequired in 2D on the reference element for a cubic finite element approximationof the solution. Note that when mapped to the real mesh from the referenceelement, each of these is just part of one of the basis functions that isactually supported on multiple elements.
Mentions: We take the hierarchical approach because it has theadvantage that on each element the basis of degree pis the same as the basis of degree p + 1 with the degree p + 1 functions removed. This lends itself toadaptive techniques, although we do not explore them here. For example, withp = 3 on a 1Dreference element [0, 1] we havex,1-x,x(1-x)andx(1-x)12-xwhich are the two components of a linear basis function, thequadratic and the cubic respectively. In 2D the analogous approach has threelinear, three quadratic and four cubic basis functions partially or whollysupported on each element; see Fig.1 for some ofthese.

Bottom Line: We detail the hurdles which must be overcome in order to achieve theoretically-optimal errors in the approximations generated, including the choice of method for approximating the solution to the cardiac cell model component.We place our work on a solid theoretical foundation and show that it can greatly improve the accuracy in the approximation which can be achieved in a given amount of processor time.Our results demonstrate superior accuracy over linear finite elements at a cheaper computational cost and thus indicate the potential indispensability of our approach for large-scale cardiac simulation.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer Science, University of Oxford, Oxford, United Kingdom.

ABSTRACT
We present an application of high order hierarchical finite elements for the efficient approximation of solutions to the cardiac monodomain problem. We detail the hurdles which must be overcome in order to achieve theoretically-optimal errors in the approximations generated, including the choice of method for approximating the solution to the cardiac cell model component. We place our work on a solid theoretical foundation and show that it can greatly improve the accuracy in the approximation which can be achieved in a given amount of processor time. Our results demonstrate superior accuracy over linear finite elements at a cheaper computational cost and thus indicate the potential indispensability of our approach for large-scale cardiac simulation.

No MeSH data available.