A Galerkin approach to boundary element elastoplastic analysis
Computer Methods in Applied Mechanics and Engineering
H2-matrix approximation of integral operators by interpolation
Applied Numerical Mathematics
Hybrid cross approximation of integral operators
Numerische Mathematik
The Fast Solution of Boundary Integral Equations (Mathematical and Analytical Techniques with Applications to Engineering)
Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems
Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems
Fast multipole method applied to elastostatic BEM-FEM coupling
Computers and Structures
Fast Evaluation of Volume Potentials in Boundary Element Methods
SIAM Journal on Scientific Computing
Implicit procedures for the solution of elastoplastic problems by the boundary element method
Mathematical and Computer Modelling: An International Journal
A precorrected-FFT method for electrostatic analysis of complicated 3-D structures
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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Boundary element methods offer some advantages for the simulation of tunnel excavation since the radiation condition is implicitly fulfilled and only the excavation and ground surfaces have to be discretized. Hence, large meshes and mesh truncation, as required in the finite element method, are avoided. Recently, capabilities for efficiently dealing with inelastic behavior and ground support have been developed, paving the way for the use of the method to simulate tunneling. However, for large scale three dimensional problems one drawback of the boundary element method becomes prominent: the computational effort increases quadratically with the problem size. To reduce the computational effort several fast methods have been proposed. Here a fast boundary element solution procedure for small strain elasto-plasticity based on a collocation scheme and hierarchical matrices is presented. The method allows the solution of problems with the computational effort and sparse storage increasing almost linearly with respect to the problem size.