# A brief review of some application driven fast algorithms for elliptic partial differential equations

Open Mathematics (2012)

- Volume: 10, Issue: 1, page 204-216
- ISSN: 2391-5455

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topPrabir Daripa. "A brief review of some application driven fast algorithms for elliptic partial differential equations." Open Mathematics 10.1 (2012): 204-216. <http://eudml.org/doc/269003>.

@article{PrabirDaripa2012,

abstract = {Some application driven fast algorithms developed by the author and his collaborators for elliptic partial differential equations are briefly reviewed here. Subsequent use of the ideas behind development of these algorithms for further development of other algorithms some of which are currently in progress is briefly mentioned. Serial and parallel implementation of these algorithms and their applications to some pure and applied problems are also briefly reviewed.},

author = {Prabir Daripa},

journal = {Open Mathematics},

keywords = {Fast algorithms; Numerical methods; Elliptic equations; fast algorithms; numerical methods; elliptic equations},

language = {eng},

number = {1},

pages = {204-216},

title = {A brief review of some application driven fast algorithms for elliptic partial differential equations},

url = {http://eudml.org/doc/269003},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Prabir Daripa

TI - A brief review of some application driven fast algorithms for elliptic partial differential equations

JO - Open Mathematics

PY - 2012

VL - 10

IS - 1

SP - 204

EP - 216

AB - Some application driven fast algorithms developed by the author and his collaborators for elliptic partial differential equations are briefly reviewed here. Subsequent use of the ideas behind development of these algorithms for further development of other algorithms some of which are currently in progress is briefly mentioned. Serial and parallel implementation of these algorithms and their applications to some pure and applied problems are also briefly reviewed.

LA - eng

KW - Fast algorithms; Numerical methods; Elliptic equations; fast algorithms; numerical methods; elliptic equations

UR - http://eudml.org/doc/269003

ER -

## References

top- [1] Anderes E., Coram M.A., Two-dimensional density estimation using smooth invertible transformation, J. Statist. Plann. Inference, 2011, 141(3), 1183–1193 http://dx.doi.org/10.1016/j.jspi.2010.09.019 Zbl1206.62057
- [2] Badea L., Daripa P., On a boundary control approach to domain embedding method, SIAM J. Control Optim., 2001, 40(2), 421–449 http://dx.doi.org/10.1137/S0363012999357380 Zbl1002.93026
- [3] Badea L., Daripa P., A fast algorithm for two-dimensional elliptic problems, Numer. Algorithms, 2002, 30(3–4), 199–239 http://dx.doi.org/10.1023/A:1020176803736 Zbl1079.65123
- [4] Badea L., Daripa P., On a Fourier method of embedding domains using an optimal distributed control, Numer. Algorithms, 2003, 32(2–4), 261–273 http://dx.doi.org/10.1023/A:1024002802603 Zbl1079.65124
- [5] Badea L., Daripa P., A domain embedding method using the optimal distributed control and a fast algorithm, Numer. Algorithms, 2004, 36(2), 95–112 http://dx.doi.org/10.1023/B:NUMA.0000033094.75324.48 Zbl1052.93021
- [6] Borges L., Daripa P., A parallel version of a fast algorithm for singular integral transforms, Numer. Algorithms, 2000, 23(1), 71–96 http://dx.doi.org/10.1023/A:1019143832124 Zbl0948.65142
- [7] Borges L., Daripa P., A fast parallel algorithm for the Poisson equation on a disk, J. Comput. Phys., 2001, 169(1), 151–192 http://dx.doi.org/10.1006/jcph.2001.6720 Zbl0980.65133
- [8] Daripa P., On applications of a complex variable method in compressible flows, J. Comput. Phys., 1990, 88(2), 337–361 http://dx.doi.org/10.1016/0021-9991(90)90183-2
- [9] Daripa P., A fast algorithm to solve nonhomogeneous Cauchy-Riemann equations in the complex plane, SIAM J. Sci. Statist. Comput., 1992, 13(6), 1418–1432 http://dx.doi.org/10.1137/0913080 Zbl0762.65013
- [10] Daripa P., A fast algorithm to solve the Beltrami equation with applications to quasiconformal mappings, J. Comput. Phys., 1993, 106(2), 355–365 Zbl0777.65010
- [11] Daripa P., Dash R.K., A numerical study of pulsatile blood flow in an eccentric catheterized artery using a fast algorithm, J. Engrg. Math., 2002, 42(1), 1–22 http://dx.doi.org/10.1023/A:1014332225766 Zbl1045.76032
- [12] Daripa P., Mashat D., Singular integral transforms and fast numerical algorithms, Numer. Algorithms, 1998, 18(2), 133–157 http://dx.doi.org/10.1023/A:1019117414918 Zbl0916.65127
- [13] Daripa P., Mashat D., An efficient and novel numerical method for quasiconformal mappings of doubly connected domains, Numer. Algorithms, 1998, 18(2), 159–178 http://dx.doi.org/10.1023/A:1019169431757 Zbl0931.30010
- [14] Du K., A simple numerical method for complex geometrical optics solutions to the conductivity equation, SIAM J. Sci. Comput., 2011, 33(1), 328–341 http://dx.doi.org/10.1137/100802256 Zbl1236.78001
- [15] Golberg M.A. (Ed.), Solution Methods for Integral Equations, Math. Concepts Methods Sci. Engrg., 18, Plenum Press, New York, 1978
- [16] Golberg M.A. (Ed.), Numerical Solution of Integral Equations, Math. Concepts Methods Sci. Engrg., 42, Plenum Press, New York, 1990
- [17] Greengard L., The Rapid Evaluation of Potential Fields in Particle Systems, ACM Disting. Diss., MIT Press, Cambridge, 1988 Zbl1001.31500
- [18] Greengard L., Kropinski M.C., Mayo A., Integral equation methods for Stokes flow and isotropic elasticity in the plane, J. Comput. Phys., 1996, 125(2), 403–414 http://dx.doi.org/10.1006/jcph.1996.0102 Zbl0847.76066
- [19] Greengard L., Rokhlin V., A fast algorithm for particle simulations, J. Comput. Phys., 1987, 73(2), 325–348 http://dx.doi.org/10.1016/0021-9991(87)90140-9 Zbl0629.65005
- [20] Greengard L., Rokhlin V., A new version of the fast multipole method for the Laplace equation in three dimensions, In: Acta Numer., 6, Cambridge University Press, Cambridge, 1997, 229–269 Zbl0889.65115
- [21] Hackbusch W., Integral Equations, Internat. Ser. Numer. Math., 120, Birkhäuser, Basel, 1995 http://dx.doi.org/10.1007/978-3-0348-9215-5 Zbl0823.65139
- [22] Hwang K., Advanced Computer Architecture: Parallelism, Scalability, Programmability, McGraw-Hill, New York, 1993
- [23] Uhlmann G., Electrical impedance tomography and Calderón’s problem, Inverse Problems, 2009, 25(12), #123011 Zbl1181.35339

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