Considering the risk of climate change, the foreseeable shortage of fossil fuels and the increasing demand for energy, the development of new energy production methods based on renewable resources is urgent. Problems with many renewable resources, though, is their dependence on certain weather conditions and their insufficient ability to provide a certain baseload. A renewable resource that does not suffer from these shortcoming is the heat stored in the Earth’s crust which can be used in geothermal facilities. This chapter gives a short introduction into geothermics, describing the basic ideas, classifying different systems which are suitable for industrial applications and discussing some of the challenges they pose to the (geo-)scientific community. These challenges are then organized from the viewpoint of geomathematics into a column model. This book is concerned with questions risen by the fourth column; the modeling of the stress field in geothermal reservoirs. We give a brief overview on literature on rock mechanics and geomechanics, followed by an outline giving the content of subsequent chapters of this book.


Fundamental Solution Boundary Element Method Land Subsidence Boundary Integral Equation Geothermal System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Abeyratne, M.K., Freeden, W., Mayer, C.: Multiscale deformation analysis by Cauchy-Navier wavelets. J. Appl. Math. 12, 605–645 (2003)MathSciNetCrossRefGoogle Scholar
  2. 5.
    Allis, R., Bromley, C., Currie, S.: Update on subsidence at the Wairakei-Tauhara geothermal system, New Zealand. Geothermics 38, 169–180 (2009)CrossRefGoogle Scholar
  3. 6.
    Allis, R.G., Zhan, X.: Predicting subsidence at Wairakei and Ohaaki geothermal fields, New Zealand. Geothermics 29, 479–497 (2000)CrossRefGoogle Scholar
  4. 13.
    Augustin, M.: Mathematical aspects of stress field simulations in deep geothermal reservoirs. Schr. Funkt.Anal. Geomath. 50, 1–26 (2011)Google Scholar
  5. 14.
    Augustin, M.: On the role of poroelasticity for modeling of stress fields in geothermal reservoirs. Int. J. Geomath. 3, 67–93 (2012)MathSciNetCrossRefGoogle Scholar
  6. 15.
    Augustin, M., Bauer, M., Blick, C., Eberle, S., Freeden, W., Gerhards, C., Ilyasov, M., Kahnt, R., Klug, M., Michel, I., Möhringer, S., Neu, T., Nutz, H., I., Punzi, A.: Modeling deep geothermal reservoirs: recent advances and future perspectives. In: W. Freeden, Z. Nashed, T. Sonar (eds.) Handbook of Geomathematics, 2nd edn. Springer, New York (2015). Accepted for publicationGoogle Scholar
  7. 17.
    Augustin, M., Freeden, W., Gerhards, C., Möhringer, S., Ostermann, I.: Mathematische Methoden in der Geothermie. Math. Semesterber. 59, 1–28 (2012)MathSciNetCrossRefGoogle Scholar
  8. 20.
    Badmus, T., Cheng, A.H.D., Grilli, S.: A Laplace-transform-based three-dimensional BEM for poroelasticity. Int. J. Numer. Method. Eng. 36, 67–85 (1993)CrossRefGoogle Scholar
  9. 21.
    Baisch, S., Carbon, D., Dannwolf, U., Delacou, B., Delvaux, M., Dunand, F., Jung, R., Koller, M., Martin, C., Sartori, M., Secanell, R., Vorös, R.: Deep heat mining Basel – seismic risk analysis. SERIANEX. Tech. rep., study prepared for the Departement für Wirtschaft, Soziales und Umwelt des Kantons Basel-Stadt, Amt für Umwelt und Energie (2009)Google Scholar
  10. 23.
    Barbier, E.: Geothermal energy technology and current status: an overview. Renew. Sustain. Energy Rev. 6, 3–65 (2002)CrossRefGoogle Scholar
  11. 32.
    Berryman, J.G.: Comparison of upscaling methods in poroelasticity and its generalizations. J. Eng. Mech. 131, 928–936 (2005)CrossRefGoogle Scholar
  12. 33.
    Bertani, R.: Geothermal power generation in the world 2005–2010 update report. Geothermics 41, 1–29 (2012)CrossRefGoogle Scholar
  13. 34.
    Biot, M.A.: Le Problème de la Consolidation des Matières Argileuses sous une Charge. Ann. Soc. Sci. Brux. B55, 110–113 (1935)Google Scholar
  14. 38.
    Biot, M.A.: Mechanics of deformation and acoustic propagation in porous media. J. Appl. Phys. 33, 1482–1498 (1962)MathSciNetCrossRefGoogle Scholar
  15. 39.
    de Boer, R.: Theoretical poroelasticity – a new approach. Chaos Solitons Fractals 25, 861–878 (2005)CrossRefGoogle Scholar
  16. 51.
    Cheng, A.H.D., Detournay, E.: A direct boundary element method for plane strain poroelasticity. Int. J. Numer. Anal. Method. Geomech. 12, 551–572 (1988)CrossRefGoogle Scholar
  17. 52.
    Cheng, A.H.D., Detournay, E.: On singular integral equations and fundamental solutions of poroelasticity. Int. J. Solid. Struct. 35, 4521–4555 (1998)MathSciNetCrossRefGoogle Scholar
  18. 53.
    Cheng, A.H.D., Liggett, J.A.: Boundary integral equation method for linear porous-elasticity with applications to soil consolidation. Int. J. Numer. Method. Eng. 20, 255–278 (1984)CrossRefGoogle Scholar
  19. 54.
    Cheng, A.H.D., Predeleanu, M.: Transient boundary element formulation for linear poroelasticity. Appl. Math. Model. 11, 285–290 (1987)MathSciNetCrossRefGoogle Scholar
  20. 57.
    Costabel, M.: Boundary integral operators for the heat equation. Integral Equ. Operat. Theory 13, 498–552 (1990)MathSciNetCrossRefGoogle Scholar
  21. 64.
    Dargush, G.F., Banerjee, P.K.: A time domain boundary element method for poroelasticity. Int. J. Numer. Method. Eng. 28, 2423–2449 (1989)CrossRefGoogle Scholar
  22. 66.
    Dickson, M.H., Fanelli, M.: Geothermal Energy. Earthscan, New York (2003)Google Scholar
  23. 67.
    Eberhart-Phillips, D., Oppenheimer, D.H.: Induced seismicity in The Geysers geothermal area, California. J. Geophys. Res. 89, 1191–1207 (1984)CrossRefGoogle Scholar
  24. 71.
    Evans, K.F., Cornet, F.H., Hashida, T., Hayashi, K., Ito, T., Matsuki, K., Wallroth, T.: Stress and rock mechanics issues of relevance to HDR/HWR engineered geothermal systems: review of developments during the past 15 years. Geothermics 28, 455–474 (1999)CrossRefGoogle Scholar
  25. 73.
    Expertengruppe “Seismisches Risiko bei hydrothermaler Geothermie”: Das seismische Ereignis bei Landau vom 15. August 2009, Abschlussbericht. Tech. rep., on behalf of the Ministerium für Umwelt, Landwirtschaft, Ernährung, Weinbau und Forsten des Landes Rheinland-Pfalz (2010)Google Scholar
  26. 78.
    Fialko, Y., Simons, M.: Deformation and seismicity in the Coso geothermal area, Inyo County, California: observations and modeling using satellite radar interferometry. J. Geophys. Res. 105, 21,781–21,793 (2000)Google Scholar
  27. 81.
    Freeden, W.: Multiscale Modelling of Spaceborne Geodata. Teubner, Stuttgart (1999)Google Scholar
  28. 82.
    Freeden, W.: Metaharmonic Lattice Point Theory. CRC Press/Taylor & Francis, Boca Raton (2011)Google Scholar
  29. 83.
    Freeden, W., Blick, C.: Signal decorrelation by means of multiscale methods. World Min. Surf. Undergr. 65, 304–317 (2013)Google Scholar
  30. 84.
    Freeden, W., Gerhards, C.: Poloidal and toroidal field modeling in terms of locally supported vector wavelets. Math. Geosci. 42, 817–838 (2010)MathSciNetCrossRefGoogle Scholar
  31. 85.
    Freeden, W., Gerhards, C.: Geomathematically Oriented Potential Theory. Chapman & Hall/CRC Press, Boca Raton (2013)Google Scholar
  32. 86.
    Freeden, W., Gervens, T., Schreiner, M.: Constructive Approximation on the Sphere (With Applications to Geomathematics). Oxford Science Publications, Oxford (1998)Google Scholar
  33. 87.
    Freeden, W., Groten, E., Schreiner, M., Söhne, W., Tücks, M.: Deformation analysis using Navier spline interpolation (with an application to the Lake Blåsjø area). Allg. Vermess.-Nachr. 3, 120–146 (1996)Google Scholar
  34. 88.
    Freeden, W., Gutting, M.: Special Functions of Mathematical (Geo-)Physics. Birkhäuser, Basel (2013)CrossRefGoogle Scholar
  35. 90.
    Freeden, W., Mayer, C., Schreiner, M.: Tree algorithms in wavelet approximations by Helmholtz potential operators. Numer. Funct. Anal. Optim. 24, 747–782 (2003)MathSciNetCrossRefGoogle Scholar
  36. 91.
    Freeden, W., Michel, V.: Multiscale Potential Theory with Applications to Geoscience. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston (2004)CrossRefGoogle Scholar
  37. 92.
    Freeden, W., Michel, V.: Wavelet deformation analysis for spherical bodies. Int. J. Wavelets, Multiresolut. Inf. Process. 3, 523–558 (2005)Google Scholar
  38. 93.
    Freeden, W., Nutz, H.: Satellite gravity gradiometry as tensorial inverse problem. Int. J. Geomath. 2, 123–146 (2011)MathSciNetCrossRefGoogle Scholar
  39. 94.
    Freeden, W., Nutz, H.: Mathematische Methoden. In: M. Bauer, W. Freeden, H. Jacobi, T. Neu (eds.) Handbuch Tiefe Geothermie. Springer, Berlin (2014)Google Scholar
  40. 95.
    Freeden, W., Ostermann, I., Augustin, M.: Mathematik als Schlüsseltechnologie in der Geothermie. Geotherm. Energ. 70, 20–24 (2011)Google Scholar
  41. 96.
    Freeden, W., Reuter, R.: A constructive method for solving the displacement boundary-value problem of elastostatics by use of global basis systems. Math. Method. Appl. Sci. 12, 105–128 (1990)MathSciNetCrossRefGoogle Scholar
  42. 97.
    Freeden, W., Schreiner, M.: Spherical Functions of Mathematical Geosciences – A Scalar, Vectorial, and Tensorial Setup. Advances in Geophysical and Environmental Mechanics and Mathematics, 1st edn. Springer, Berlin (2009)Google Scholar
  43. 98.
    Frenkel, J.: On the theory of seismic and seismoelectric phenomena in a moist soil. J. Eng. Mech. 131, 879–887 (2005). Originally published in J. Phys. 3, 230–241 (1944)Google Scholar
  44. 99.
    Fridleifsson, I.B., Freeston, D.H.: Geothermal energy research and developement. Geothermics 23, 175–214 (1992)CrossRefGoogle Scholar
  45. 100.
    Friedleifsson, I., Ragnarsson, Á.: Survey of Energy Resources, chap. 11 Geothermal Energy, pp. 427–477. World Energy Council, London (2007)Google Scholar
  46. 103.
    Gehringer, M., Loksha, V.: Geothermal Handbook: Planning and Financing Power Generation. The International Bank for Reconstruction and Development, The World Bank Group (2012). Energy Sector Management Assistance Program (ESMAP)Google Scholar
  47. 104.
    Gerhards, C.: Spherical decompositions in a global and local framework: theory and an application to geomagnetic modeling. Int. J. Geomath. 1, 205–256 (2011)MathSciNetCrossRefGoogle Scholar
  48. 108.
    Gerhards, C.: Multiscale modeling of the geomagnetic field and ionospheric currents. In: W. Freeden, Z. Nashed, T. Sonar (eds.) Handbook of Geomathematics, 2nd edn. Springer, New York (2015). Accepted for publicationGoogle Scholar
  49. 109.
    Ghassemi, A.: A review of some rock mechanics issues in geothermal reservoir developement. Geotechn. Geol. Eng. 30, 647–664 (2012)CrossRefGoogle Scholar
  50. 110.
    Ghassemi, A., Cheng, A.H.D., Diek, A., Roegiers, J.C.: A complete plane strain fictitious stress boundary element method for poroelastic media. Eng. Anal. Bound. Elem. 25, 41–48 (2001)CrossRefGoogle Scholar
  51. 112.
    Ghassemi, A., Tarasovs, S.: Fracture slip and opening in response to fluid injection into a geothermal reservoir. In: Proceedings Thirty-First Workshop on Geothermal Reservoir Engineering, Stanford (2006)Google Scholar
  52. 114.
    Glowacka, E., Sarychikhina, O., Nava, F.A.: Subsidence and stress changes in the Cerro Pietro geothermal field, B. C., Mexico. Pure Appl. Geophys. 162, 2095–2110 (2005)Google Scholar
  53. 117.
    Goldemberg, J. (ed.): World energy assesment: energy and the challenge of sustainability. United Nations Development Programme, United Nations Department of Economic and Social Affairs, World Energy Council (2000)Google Scholar
  54. 118.
    Goldemberg, J., Johansson, T.B. (eds.): World energy assesment: overview 2004 update. United Nations Development Programme, United Nations Department of Economic and Social Affairs, World Energy Council (2004)Google Scholar
  55. 123.
    Gudmundsson, A., Fjeldskaar, I., Brenner, S.L.: Propagation pathways and fluid transport of hydrofractures in jointed and layered rocks in geothermal fields. J. Volcanol. Geotherm. Res. 116, 257–278 (2002)CrossRefGoogle Scholar
  56. 125.
    Gunasekera, R.C., Foulger, G.R., Julian, B.R.: Reservoir depletion at The Geysers geothermal area, California, shown by four-dimensional seismic tomography. J. Geophys. Res: Solid Earth 108, 2156–2202 (2003)CrossRefGoogle Scholar
  57. 126.
    Haenel, R., Rybach, L., Stegana, L.: Fundamentals of geothermics. In: R. Haenel, L. Rybach, L. Stegana (eds.) Handbook of Terrestrial Heat-Flow Density Determination, pp. 9–57. Kluwer Academics, Dordrecht (1988)CrossRefGoogle Scholar
  58. 130.
    Hicks, T.W., Pine, R.J., Willis-Richards, J., Xu, S., Jupe, A.J., Rodrigues, N.E.V.: A hydro-thermo-mechanical numerical model for HDR geothermal reservoir evaluation. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 33, 499–511 (1996)CrossRefGoogle Scholar
  59. 134.
    Ilyasov, M.: A tree algorithm for Helmholtz potential wavelets on non-smooth surfaces: theoretical background and application to seismic data postprocessing. Ph.D. thesis, University of Kaiserslautern, Geomathematics Group (2011)Google Scholar
  60. 138.
    Jaeger, J.C., Cook, N.G.W., Zimmerman, R.W.: Fundamentals of Rock Mechanics, 4th edn. Blackwell, Malden (2007)Google Scholar
  61. 139.
    Jing, L., Hudson, J.A.: Numerical methods in rock mechanics. Int. J. Rock Mech. Min. Sci. 39, 409–427 (2002)CrossRefGoogle Scholar
  62. 143.
    Johansson, B.T., Lesnic, D., Reeve, T.: A method of fundamental solutions for two-dimensional heat conduction. Int. J. Comput. Math. 88, 1697–1713 (2011)MathSciNetCrossRefGoogle Scholar
  63. 146.
    Jung, R.: Stand und Aussichten der Tiefengeothermie in Deutschland. Erdöl, Erdgas, Kohle 123, 1–7 (2007)Google Scholar
  64. 161.
    Kohl, T., Brenni, R., Eugster, W.: System performance of a deep borehole heat exchanger. Geothermics 31, 687–708 (2002)CrossRefGoogle Scholar
  65. 163.
    Kupradze, V.D.: A method for the approximate solution of limiting problems in mathematical physics. USSR Comput. Math. Math. Phys. 4, 199–205 (1964)CrossRefGoogle Scholar
  66. 169.
    Lai, M., Krempl, E., Ruben, D.: Introduction to Continuum Mechanics, 4th edn. Butterworth-Heinemann, Oxford (2010)Google Scholar
  67. 170.
    Landau, L.D., Pitaevskii, L.P., Lifshitz, E.M., Kosevich, A.M.: Theory of Elasticity. Theoretical Physics, vol. 7, 3rd edn. Butterworth-Heinemann, Oxford (1986)Google Scholar
  68. 175.
    Lions, J.L.: Equations Differentielles Operationelles et Problèmes aux Limites. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, vol. 111. Springer, Berlin (1961)Google Scholar
  69. 177.
    Lopatnikov, S.L., Gillespie, J.W., Jr.: Poroelasticity-I: governing equations of the mechanics of fluid-saturated porous material. Transp. Porous Media 84, 471–492 (2010)MathSciNetCrossRefGoogle Scholar
  70. 178.
    Lopatnikov, S.L., Gillespie, J.W., Jr.: Poroelasticity-II: on the equilibrium state of the fluid-filled penetrable poroelastic body. Transp. Porous Media 89, 475–486 (2011)MathSciNetCrossRefGoogle Scholar
  71. 179.
    Lopatnikov, S.L., Gillespie, J.W., Jr.: Poroelasticity-III: conditions on the interface. Transp. Porous Media 93, 597–607 (2012)MathSciNetCrossRefGoogle Scholar
  72. 182.
    Luchko, Y., Punzi, A.: Modeling anomalous heat transport in geothermal reservoirs via fractional diffusion equations. Int. J. Geomath. 1, 257–276 (2011)MathSciNetCrossRefGoogle Scholar
  73. 183.
    Lund, J.W.: Direct utilization of geothermal energy. Energies 3, 1443–1471 (2010)CrossRefGoogle Scholar
  74. 188.
    Marsden, J.E., Hughes, T.J.R.: Mathematical Foundations of Elasticity. Dover, Mineola (1994)Google Scholar
  75. 192.
    Mayer, C., Freeden, W.: Stokes problem, layer potentials and regularizations, multiscale applications. In: W. Freeden, Z. Nashed, T. Sonar (eds.) Handbook of Geomathematics, 2nd edn. Springer, New York (2015). Accepted for publicationGoogle Scholar
  76. 197.
    Menéndez, C., Nieto, P.J.G., Ortega, F.A., Bello, A.: Mathematical modelling and study of the consolidation of an elastic saturated soil with an incompressible fluid by FEM. Math. Comput. Model. 49, 2002–2018 (2009)CrossRefGoogle Scholar
  77. 201.
    Möhringer, S.: Decorrelation of gravimetric data. Ph.D. thesis, University of Kaiserslautern, Geomathematics Group (2014)Google Scholar
  78. 202.
    Moldovan, I.D., Teixera de Freitas, J.A.: Hybrid-trefftz stress and displacement elements for dynamic analysis of bounded and unbounded saturated porous media. Comput. Assist. Mech. Eng. Sci. 15, 289–303 (2008)Google Scholar
  79. 204.
    Mosconi, M.: A variational approach to porous elastic bodies. Z. Angew. Math. Phys. ZAMP 56, 548–558 (2005)MathSciNetCrossRefGoogle Scholar
  80. 205.
    Mossop, A., Segall, P.: Subsidence at The Geysers geothermal field, N. California from a comparison of GPS and leveling surveys. Geophys. Res. Lett. 24, 1839–1842 (1997)Google Scholar
  81. 209.
    Naumovich, A.: Efficient numerical methods for the Biot poroelasticity system in multilayered domains. Ph.D. thesis, University of Kaiserslautern, Department of Mathematics (2007)Google Scholar
  82. 214.
    Ostermann, I.: A mathematical model for 3D heat transport in hydrothermal systems. World Min. Surf. Undergr. 63, 280–289 (2011)Google Scholar
  83. 216.
    Ostermann, I.: Three-dimensional modeling of heat transport in deep hydrothermal reservoirs. Int. J. Geomath. 2, 37–68 (2011)MathSciNetCrossRefGoogle Scholar
  84. 220.
    Paschen, H., Oertel, D., Grünwald, R.: Möglichkeiten geothermischer Stromerzeugung in Deutschland. TAB Arbeitsbericht 84, Deutscher Bundestag, Ausschuss für Bildung, Forschung und Technikfolgeabschätzung (2003)Google Scholar
  85. 221.
    Phillips, P.J.: Finite element method in linear poroelasticity: theoretical and computational results. Ph.D. thesis, University of Texas, Austin (2005)Google Scholar
  86. 225.
    Phillips, P.J., Wheeler, M.F.: Overcoming the problem of locking in linear elasticity and poroelasticity: an heuristic approach. Comput. Geosci. 13, 5–12 (2009)CrossRefGoogle Scholar
  87. 234.
    Renardy, M., Rogers, R.C.: An Introduction to Partial Differential Equations. Texts in Applied Mathematics. Springer, New York (1993)Google Scholar
  88. 240.
    Rutqvist, J., Stephansson, O.: The role of hydromechanical coupling in fractured rock engineering. Hydrogeol. J. 11, 7–40 (2003)CrossRefGoogle Scholar
  89. 241.
    Saemundsson, K., Axelsson, G., Steingrimsson, B.: Geothermal systems in global perspectives. In: Short Course V on Conceptual Modelling of Geothermal Systems. United Nations University Geothermal Training Programme, La Geo, Santa Tecla, El Salvador (2013)Google Scholar
  90. 243.
    Sanyal, S.K.: Classification of geothermal systems – a possible scheme. In: Proceedings of the Thirtieth Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford (2005)Google Scholar
  91. 247.
    Schanz, M.: Application of 3D time domain boundary element formulation to wave propagation in poroelastic solids. Eng. Anal. Bound. Elem. 25, 363–376 (2001)CrossRefGoogle Scholar
  92. 249.
    Schellschmidt, R., Sanner, B., Pester, S., Schulz, R.: Geothermal energy use in Germany. In: Proceedings World Geothermal Congress, Bali (2010)Google Scholar
  93. 250.
    Schulz, R.: Aufbau eines geothermischen Informationssystems für Deutschland. Tech. Rep., Leibniz-Institut für Angewandte Geophysik, Hannover (2009)Google Scholar
  94. 251.
    Selvadurai, A.P.S.: The analytical method in geomechanics. Appl. Mech. Rev. 60, 87–106 (2007)CrossRefGoogle Scholar
  95. 254.
    Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251, 310–340 (2000)MathSciNetCrossRefGoogle Scholar
  96. 260.
    Skopetskii, V.V., Marchenko, O.A.: Formulation and analysis of problems for dynamic systems of inhomogeneous two-phase media. Cybern. Syst. Anal. 41, 865–878 (2005)MathSciNetCrossRefGoogle Scholar
  97. 262.
    Smyrlis, Y.S.: Applicability and applications of the method of fundamental solutions. Math. Comput. 78, 1399–1434 (2009)MathSciNetCrossRefGoogle Scholar
  98. 264.
    Smyrlis, Y.S.: Mathematical foundation of the MFS for certain elliptic systems in linear elasticity. Numer. Math. 112, 319–340 (2009)MathSciNetCrossRefGoogle Scholar
  99. 271.
    von Terzaghi, K.: Die Berechnung der Durchlässigkeitsziffer des Tones aus dem Verlauf der hydrodynamischen Spannungserscheinungen. Sitz.-ber. Akad. Wiss., Wien, Math.-Nat.-wiss. Kl., Abt. IIa 132, 105–124 (1923)Google Scholar
  100. 272.
    von Terzaghi, K.: Theoretical Soil Mechanics. Wiley, New York (1943)CrossRefGoogle Scholar
  101. 273.
    Tester, J.W., Anderson, B.J., Batchelor, A.S., Blackwell, D.D., DiPippo, R., Drake, E.M., Garnish, J., Livesay, B., Moore, M.C., Nichols, K., Petty, S., Toksösz, M.N., Veatch Jr., R.W., Baria, R., Augustine, C., Murphy, E., Negraru, P., Richards, M.: The Future of geothermal energy. Tech. Rep., Idaho National Laboratory, copyright by Massachussetts Institute of Technology (2006)Google Scholar
  102. 282.
    Vgenopoulou, I., Beskos, D.E.: Dynamic behavior of saturated poroviscoelastic media. Acta Mech. 95, 185–195 (1992)CrossRefGoogle Scholar
  103. 286.
    Wang, W., Kosakowski, G., Kolditz, O.: A parallel finite element scheme for thermo-hydro-mechanical (THM) coupled problems in porous media. Comput. Geosci. 35, 1631–1641 (2009)CrossRefGoogle Scholar
  104. 290.
    Wiebe, T., Antes, H.: A time domain integral formulation of dynamic poroelasticity. Acta Mech. 90, 125–137 (1991)MathSciNetCrossRefGoogle Scholar
  105. 303.
    Zhou, X.X., Ghassemi, A.: Three-dimensional poroelastic simulation of hydraulic and natural fractures using the displacement discontinuity method. In: Proceedings Thirty-Fourth Workshop on Geothermal Reservoir Engineering, Stanford (2009)Google Scholar
  106. 304.
    Zubkov, V.V., Koshelev, V.F., Lin’kov, A.M.: Numerical modeling of hydraulic fracture initiation and developement. J. Min. Sci. 43, 40–56 (2007)CrossRefGoogle Scholar

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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Matthias Albert Augustin
    • 1
  1. 1.AG GeomathematikTechnische Universität KaiserslauternKaiserslauternGermany

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