Many innovative floating offshore structures have been proposed for cost effectiveness of oil and gas exploration and production in water depths exceeding one thousand meters in recent years. One such type of platform is the offshore floating Spar platform. The Spar platform is modelled as a rigid body with six degrees-of-freedom, connected to the sea floor by multicomponent catenary mooring li...

A robust and fast solver for the fractional differential equation (FDEs) involving the Riesz fractional derivative is developed using an adaptive finite element method on nonuniform meshes. It is based on the utilization of hierarchical matrices (H-Matrices) for the representation of the stiffness matrix resulting from the finite element discretization of the FDEs. We employ a geometric multigr...

In this article we present the first results on domain decomposition methods for nonlocal operators. We present a nonlocal variational formulation for these operators and establish the well-posedness of associated boundary value problems, proving a nonlocal Poincaré inequality. To determine the conditioning of the discretized operator, we prove a spectral equivalence which leads to a mesh size ...

Inversion of Scholte wave is one of the most common methods to estimate the shear speeds in the bottom. This inversion involves running a forward model, with shear speeds in the sediment among the input parameters, and minimizing the data-model mismatch. A numerical model is developed based on the dynamic stiffness matrix approach to model the phase velocity dispersion of Scholte waves in this ...

In this paper we present a family of scalable preconditioners for matrices arising in the discretization of H(div) problems using the lowest order Raviart-Thomas finite elements. Our approach belongs to the class of “auxiliary space”-based methods and requires only the finite element stiffness matrix plus some minimal additional discretization information about the topology and orientation of m...

A simple method to follow the postbuckling paths in the finite element analysis is presented. During a standard path-following by means of arc-length method, the signs of diagonal elements in the triangularized tangent stiffness matrix are monitored to determine the existence of singular points between two adjacent solution points on paths. A simple approach to identify limit or bifurcation poi...

– Building on the well-established form closure framework for holding rigid parts, this paper proposes a new framework for holding deformable parts. We consider the class of deformable parts that can be modeled as linearly elastic polygons with a triangular finite element mesh and given stiffness matrix. We define the D-space (deformation-space) of a part as the C-space of all its mesh nodes. F...

Additive Schwarz preconditioners are developed for the h-version of the boundary element method for the hypersingular integral equation on surfaces in three dimensions. The first preconditioner consists of decomposing into local spaces associated with the subdomain interiors, supplemented with a wirebasket space associated with the the subdomain interfaces. The wirebasket correction only involv...

As a semi-analytical structural analysis algorithm, the scaled boundary finite-element method (SBFEM) only discretizes the boundary of the analyzed domain without the need of fundamental solutions, which makes it powerful for problems with stress singularity or unbounded foundation media. In this paper, a sensitivity analysis method of SBFEM is proposed for elastostatics, through which the firs...