dc.contributor.author |
Nadukandi, Prashanth |
dc.date |
2015-05 |
dc.identifier.citation |
Nadukandi, P. Numerically stable formulas for a particle-based explicit exponential integrator. "Computational mechanics", Maig 2015, vol. 55, núm. 5, p. 903-920. |
dc.identifier.citation |
0178-7675 |
dc.identifier.citation |
10.1007/s00466-015-1142-5 |
dc.identifier.uri |
http://hdl.handle.net/2117/87031 |
dc.language.iso |
eng |
dc.relation |
http://link.springer.com/article/10.1007%2Fs00466-015-1142-5 |
dc.rights |
info:eu-repo/semantics/openAccess |
dc.subject |
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits |
dc.subject |
Finite element method |
dc.subject |
X-IVAS scheme
Particle finite element method
Explicit exponential integrators
Tangent curves
Closed-form analytical solutions
Finite arithmetic
Loss of significance
Numerically stable formulas |
dc.subject |
Elements finits, Mètode dels |
dc.title |
Numerically stable formulas for a particle-based explicit exponential integrator |
dc.type |
info:eu-repo/semantics/submittedVersion |
dc.type |
info:eu-repo/semantics/article |
dc.description.abstract |
The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-015-1142-5 |
dc.description.abstract |
Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this scheme involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function. |
dc.description.abstract |
Peer Reviewed |