Treatment of singularities in time-dependent problems using the boundary element method

Keywords

Singularity, Boundary element method, Gravitational singularity, Mathematical analysis, Mathematics

References

• Boundary element researchC. A. Brebbia — 1985
• The Mathematics Of DiffusionJohn Crank — 1956
• Corner singularities in elliptic problems by finite element methodsR. Wait, Andrew Mitchell — 1971
• Convergence of finite-difference techniques for a harmonic mixed boundary value problemJ. R. Whiteman, Jerry Claude Webb — 1970
• A Note on One-Dimensional Constant-Head Permeability TestsZ. A. Al-Dhahir, Shanshan Tan — 1968
• Handbook of Mathematical Functions.Juliette Florentin, Milton Abramowitz, Irene A. Stegun — 1966
• A method of treating boundary singularities in time-dependent problemsGraham E. C. Bell, J Crank — 1973
• The treatment of singularities of partial differential equations by relaxation methodsH. Motz — 1947
• Boundary Elements IXC. A. Brebbia, Wolfgang L. Wendland, G. Kühn — 1987
• Handbook of Mathematical FunctionsDonald A. McQuarrie — 1966
• Applications of the boundary element method for heat transfer problemsC. Brebbia — 1985
• Time Dependent Non-Linear Potential ProblemsP. Škerget, C. Brebbia — 1985

Cited by

• The method of fundamental solutions for some direct and inverse problemsThomas Reeve — 2013
• A Boundary Meshless Method for Solving Heat Transfer Problems Using the Fourier TransformA. Tadeu, C. S. Chen, Julieta António — 2011
• Stable MFS Solution to Singular Direct and Inverse Problems Associated with the Laplace Equation Subjected to Noisy DataLiviu Marin — 2008
• Numerical approximation of the one-dimensional inverse Cauchy–Stefan problem using a method of fundamental solutionsTomas Johansson, D. Lesnic, Thomas Reeve — 2011
• Numerical solution of parabolic Cauchy problems in planar corner domainsRoman Chapko, Tomas Johansson, Vasyl Vavrychuk — 2014
• Transient heat conduction in homogeneous and non-homogeneous materials by the Laplace transform Galerkin boundary element methodAlok Sutradhar, Gláucio H. Paulino, L. J. Gray — 2002
• Solving transient diffusion problems: time-dependent fundamental solution approaches versus LTDRM approachesSong‐Ping Zhu — 1998
• Fundamental solutions for transient heat transfer by conduction and convection in an unbounded, half-space, slab and layered media in the frequency domainNuno Simões, A. Tadeu — 2005
• An Element-Free Galerkin Scaled Boundary Method for Steady-State Heat Transfer ProblemsYiqian He, Haitian Yang, Andrew Deeks — 2013
• A method of fundamental solutions for transient heat conductionTomas Johansson, D. Lesnic — 2008
• Experimental validation of a frequency domain BEM model to study 2D and 3D heat transfer by conductionI. Simões, Nuno Simões, A. Tadeu — 2012
• 3D transient heat conduction in multilayer systems – Experimental validation of semi-analytical solutionNuno Simões, I. Simões, A. Tadeu — 2012
• Treatment of singularities in Helmholtz-type equations using the boundary element methodLiviu Marin, D. Lesnic, V. Mantič — 2004
• A CQM-based BEM for transient heat conduction problems in homogeneous materials and FGMsA.I. Abreu, Alfredo Canelas, W.J. Mansur — 2013
• Conduction and convection phenomena through a slab with thermal heterogeneitiesA. Tadeu, Nuno Simões — 2007
• Transient heat conduction under nonzero initial conditions: A solution using the boundary element method in the frequency domainNuno Simões, A. Tadeu, Julieta António — 2012
• A method of fundamental solutions for transient heat conduction in layered materialsTomas Johansson, D. Lesnic — 2009
• Coupling BEM/TBEM and MFS for the simulation of transient conduction heat transferA. Tadeu, Nuno Simões, I. Simões — 2010
• 3D Transient Heat Transfer by Conduction and Convection across a 2D Medium using a Boundary Element ModelNuno Sim o es, A. Tadeu — 2005
• Conduction heat transfer with nonzero initial conditions using the Boundary Element Method in the frequency domainNuno Simões, A. Tadeu, W.J. Mansur — 2006

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