1,597 research outputs found
Modeling elastic wave propagation in fluid-filled boreholes drilled in nonhomogeneous media: BEM – MLPG versus BEM-FEM coupling
The efficiency of two coupling formulations, the boundary element method (BEM)-meshless local Petrov–Galerkin (MLPG) versus the BEM-finite element method (FEM), used to simulate the elastic wave propagation in fluid-filled boreholes generated by a blast load, is compared. The longitudinal geometry is assumed to be invariant in the axial direction (2.5D formulation). The material properties in the vicinity of the borehole are assumed to be nonhomogeneous as a result of the construction process and the ageing of the material. In both models, the BEM is used to tackle the propagation within the fluid domain inside the borehole and the unbounded homogeneous domain. The MLPG and the FEM are used to simulate the confined, damaged, nonhomogeneous, surrounding borehole, thus utilizing the advantages of these methods in modeling nonhomogeneous bounded media. In both numerical techniques the coupling is accomplished directly at the nodal points located at the common interfaces. Continuity of stresses and displacements is imposed at the solid–solid interface, while continuity of normal stresses and displacements and null shear stress are prescribed at the fluid–solid interface. The performance of each coupled BEM-MLPG and BEM-FEM approach is determined using referenced results provided by an analytical solution developed for a circular multi-layered subdomain. The comparison of the coupled techniques is evaluated for different excitation frequencies, axial wavenumbers and degrees of freedom (nodal points).Ministerio de Economía y Competitividad BIA2013-43085-PCentro Informático Científico de Andalucía (CICA
A New Transition Technique for the Combination of Meshfree Methods with other Numerical Methods from Macro- to Nano-Scales
Coupling the meshfree methods with othe numerical methods has good potential in computational mechanics. In this paper, to ensure the compatibility conditions for not only displacements but also its gradients, a new transition technique is proposed based on the penalty method and the transition particles. The bridge regions are used to connect the domains of different methods. The high-order compatibility conditions are satisfied through some regularly distributed transition particles. The new transition technique has several advantages: 1) through the use of the transition particles, the nodes (or atoms) in the transition region are totally independent, which will reduce significantly the cost for the node generation in the transition region; 2) the compatibility conditions in the transition region can be conveniently controlled through the adjustment of the number and distribution of the transition particles; 3) the compatibility of higher order derivatives can be easily satisfied. Several problems of fracture mechanics and multiscale analyses for solids are simulated by the newly developed coupled methods. Some key parameters used in the transition technique have been thoroughly studied and recommended. It has been demonstrated that the new transition technique is very accurate and stable, and it has very good potential to become a practical modeling and simulation tool for engineering
Isogeometric FEM-BEM coupled structural-acoustic analysis of shells using subdivision surfaces
We introduce a coupled finite and boundary element formulation for acoustic
scattering analysis over thin shell structures. A triangular Loop subdivision
surface discretisation is used for both geometry and analysis fields. The
Kirchhoff-Love shell equation is discretised with the finite element method and
the Helmholtz equation for the acoustic field with the boundary element method.
The use of the boundary element formulation allows the elegant handling of
infinite domains and precludes the need for volumetric meshing. In the present
work the subdivision control meshes for the shell displacements and the
acoustic pressures have the same resolution. The corresponding smooth
subdivision basis functions have the continuity property required for the
Kirchhoff-Love formulation and are highly efficient for the acoustic field
computations. We validate the proposed isogeometric formulation through a
closed-form solution of acoustic scattering over a thin shell sphere.
Furthermore, we demonstrate the ability of the proposed approach to handle
complex geometries with arbitrary topology that provides an integrated
isogeometric design and analysis workflow for coupled structural-acoustic
analysis of shells
Numerical analysis of a transmission problem with Signorini contact using mixed-FEM and BEM
© EDP Sciences, SMAI 2011This paper is concerned with the dual formulation of the interface problem consisting of a linear partial differential equation with variable coefficients in some bounded Lipschitz domain Ω in
Rn (n ≥ 2) and the Laplace equation with some radiation condition in the unbounded exterior domain Ωc := Rn\ ̄Ω. The two problems are coupled by transmission and Signorini contact conditions on the interface Γ = ∂Ω. The exterior part of the interface problem is rewritten using a Neumann to Dirichlet mapping (NtD) given in terms of boundary integral operators. The resulting variational formulation becomes a variational inequality with a linear operator. Then we treat the corresponding numerical scheme and discuss an approximation of the NtD mapping with an appropriate discretization of the inverse Poincar´e-Steklov operator. In particular, assuming some abstract approximation properties and a discrete inf-sup condition, we show unique solvability of the discrete scheme and obtain the corresponding a-priori error estimate. Next, we prove that these assumptions are satisfied with Raviart- Thomas elements and piecewise constants in Ω, and continuous piecewise linear functions on Γ. We suggest a solver based on a modified Uzawa algorithm and show convergence. Finally we present some numerical results illustrating our theory
On stability of discretizations of the Helmholtz equation (extended version)
We review the stability properties of several discretizations of the
Helmholtz equation at large wavenumbers. For a model problem in a polygon, a
complete -explicit stability (including -explicit stability of the
continuous problem) and convergence theory for high order finite element
methods is developed. In particular, quasi-optimality is shown for a fixed
number of degrees of freedom per wavelength if the mesh size and the
approximation order are selected such that is sufficiently small and
, and, additionally, appropriate mesh refinement is used near
the vertices. We also review the stability properties of two classes of
numerical schemes that use piecewise solutions of the homogeneous Helmholtz
equation, namely, Least Squares methods and Discontinuous Galerkin (DG)
methods. The latter includes the Ultra Weak Variational Formulation
EIT Reconstruction Algorithms: Pitfalls, Challenges and Recent Developments
We review developments, issues and challenges in Electrical Impedance
Tomography (EIT), for the 4th Workshop on Biomedical Applications of EIT,
Manchester 2003. We focus on the necessity for three dimensional data
collection and reconstruction, efficient solution of the forward problem and
present and future reconstruction algorithms. We also suggest common pitfalls
or ``inverse crimes'' to avoid.Comment: A review paper for the 4th Workshop on Biomedical Applications of
EIT, Manchester, UK, 200
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