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1

Liu, Yijun. Fast multipole boundary element method: Theory and applications in engineering. Cambridge: Cambridge University Press, 2009.

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2

Langer, Ulrich, Martin Schanz, Olaf Steinbach y Wolfgang L. Wendland, eds. Fast Boundary Element Methods in Engineering and Industrial Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25670-7.

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3

Langer, Ulrich. Fast Boundary Element Methods in Engineering and Industrial Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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4

Bond, Dave M. Fast wavelet transforms for matrices arising from boundary element methods. Ithaca, N.Y: Cornell Theory Center, Cornell University, 1994.

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5

Sauter, Stefan A. y Christoph Schwab. Boundary Element Methods. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-540-68093-2.

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6

Kobayashi, S. y N. Nishimura, eds. Boundary Element Methods. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-06153-4.

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7

Gwinner, Joachim y Ernst Peter Stephan. Advanced Boundary Element Methods. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-92001-6.

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8

Cruse, Thomas A., ed. Advanced Boundary Element Methods. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-83003-7.

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9

Annigeri, Balkrishna S. y Kadin Tseng, eds. Boundary Element Methods in Engineering. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-84238-2.

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10

Subrata, Mukherjee, ed. Boundary element methods in manufacturing. New York: Oxford University Press, 1997.

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11

E, Beskos D., ed. Boundary element methods in mechanics. Amsterdam: North-Holland, 1987.

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12

D, Ciskowski R. y Brebbia C. A, eds. Boundary element methods in acoustics. Southampton: Computational Mechanics Publications, 1991.

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13

Kythe, P. K. Introduction to boundary element methods. Boca Raton: CRC Press, 1995.

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14

Manolis, G. D. Boundary element methods in elastodynamics. London: Unwin Hyman, 1988.

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15

Hall, W. S. The boundary element method. Dordrecht: Kluwer Academic Publishers, 1994.

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16

International Conference on Boundary Element Technology (6th 1991 Southampton, England). Boundary element technology VI. Editado por Brebbia C. A. 1938-. Southampton: Computational Mechanics co-published with Elsevier Ap pliedScience, 1991.

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17

Ying, Lung-an. Infinite element methods. Beijing: Peking University Press, 1995.

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18

International Conference on Boundary Element Methods (16th 1994 Southampton, England). Boundary element method XVI. Editado por Brebbia C. A. Southhampton: Computational Mechanics Publications, 1994.

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19

Sutradhar, Alok. Symmetric galerkin boundary element method. Berlin: Springer, 2008.

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20

Wrobel, L. C. y C. A. Brebbia, eds. Boundary Element Methods in Heat Transfer. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2902-2.

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21

Hackbusch, Wolfgang, ed. Numerical Techniques for Boundary Element Methods. Wiesbaden: Vieweg+Teubner Verlag, 1992. http://dx.doi.org/10.1007/978-3-663-14005-4.

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22

Manolis, George D. y D. Polyzos, eds. Recent Advances in Boundary Element Methods. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-1-4020-9710-2.

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23

1952-, Wrobel L. C. y Brebbia C. A, eds. Boundary element methods in heat transfer. Southampton: Computational Mechanics Publications, 1992.

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24

Balaš, Ján. Stress analysis by boundary element methods. Amsterdam: Elsevier, 1989.

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25

A, Brebbia C. y Aliabadi M. H, eds. Adaptive finite and boundary element methods. Southampton: Computational Mechanics Publications, 1993.

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26

Kythe, Prem K. An introduction to boundary element methods. Boca Raton: CRC Press, 1995.

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27

Wrobel, L. C. Boundary Element Methods in Heat Transfer. Dordrecht: Springer Netherlands, 1992.

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28

K, Banerjee P. The boundary element methods in engineering. 2a ed. London: McGraw-Hill, 1994.

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29

Bonnet, Marc. Mathematical Aspects of Boundary Element Methods. Boca Raton: Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9780429332449.

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30

E, Beskos D. y American Society of Civil Engineers. Structural Division. Committee on Electronic Computation., eds. Boundary element methods in structural analysis. New York, N.Y: ASCE, 1989.

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31

International Conference on Boundary Element Methods (10th 1988 Southampton). Boundary Elements X. Southampton: Computational Mechanics Publications, 1988.

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32

Rjasanow, Sergej y Olaf Steinbach. Fast Solution of Boundary Integral Equations. Springer, 2010.

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33

Fast Boundary Element Methods In Engineering And Industrial Applications. Springer, 2012.

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34

Liu, Yijun. Fast Multipole Boundary Element Method: Theory and Applications in Engineering. Cambridge University Press, 2010.

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35

Liu, Yijun. Fast Multipole Boundary Element Method: Theory and Applications in Engineering. Cambridge University Press, 2009.

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36

Liu, Yijun. Fast Multipole Boundary Element Method: Theory and Applications in Engineering. Cambridge University Press, 2009.

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37

Liu, Yijun. Fast Multipole Boundary Element Method: Theory and Applications in Engineering. Cambridge University Press, 2009.

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38

Liu, Yijun. Fast Multipole Boundary Element Method: Theory And Applications In Engineering. Cambridge University Press, 2014.

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39

Shanker, Balasubramaniam y Eric Michielssen. Fast Time Domain Integral Equation Solvers. Wiley & Sons, Incorporated, John, 2018.

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40

Rjasanow, Sergej y Olaf Steinbach. The Fast Solution of Boundary Integral Equations (Mathematical and Analytical Techniques with Applications to Engineering). Springer, 2007.

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41

Steinbach, Olaf, Wolfgang L. Wendland, Ulrich Langer y Martin Schanz. Fast Boundary Element Methods in Engineering and Industrial Applications. Springer, 2014.

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42

Boundary Element Methods. Elsevier, 1990. http://dx.doi.org/10.1016/c2009-0-11170-4.

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43

Schwab, Christoph y Stefan A. Sauter. Boundary Element Methods. Springer London, Limited, 2010.

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44

Schwab, Christoph y Stefan A. Sauter. Boundary Element Methods. Springer, 2012.

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45

Boundary Element Methods. Academic Press, 1992.

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46

Boudreau, Joseph F. y Eric S. Swanson. Continuum dynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0019.

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Resumen
The theory and application of a variety of methods to solve partial differential equations are introduced in this chapter. These methods rely on representing continuous quantities with discrete approximations. The resulting finite difference equations are solved using algorithms that stress different traits, such as stability or accuracy. The Crank-Nicolson method is described and extended to multidimensional partial differential equations via the technique of operator splitting. An application to the time-dependent Schrödinger equation, via scattering from a barrier, follows. Methods for solving boundary value problems are explored next. One of these is the ubiquitous fast Fourier transform which permits the accurate solution of problems with simple boundary conditions. Lastly, the finite element method that is central to modern engineering is developed. Methods for generating finite element meshes and estimating errors are also discussed.
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47

Wrobel, L. C. y M. H. Aliabadi. The Boundary Element Method, The Boundary Element Method. Wiley, 2002.

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48

Cruse, Thomas A. Advanced Boundary Element Methods. Springer, 2012.

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49

Boundary Element Methods in Nonlinear Fluid Dynamics: Developments in boundary element methods - 6 (Developments in Boundary Element Methods). Routledge, 1990.

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50

Advanced Dynamic Analysis by Boundary Element Methods : Developments in Boundary Element Methods. Routledge, 1990.

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