We present a novel approach to fast on-the-fly low order finite element assembly for scalar elliptic partial differential equations of Darcy type with variable coefficients optimized for matrix-free implementations. Our approach introduces a new operator that is obtained by appropriately scaling the reference stiffness matrix from the constant coefficient case. Assuming sufficient regularity, a...

A simple technique is given in this paper for the construction and analysis of a class of finite element discretizations for convection-diffusion problems in any spatial dimension by properly averaging the PDE coefficients on element edges. The resulting finite element stiffness matrix is an M -matrix under some mild assumption for the underlying (generally unstructured) finite element grids. A...

This paper describes a stiffness analysis of a 6-RSS parallel manipulator by using matrix structural analysis. The stiffness analysis is based on standard concepts of static elastic deformations. The formulation has been implemented in order to obtain the stiffness matrix that can be numerically computed by defining a suitable model of the manipulator, which takes into account the stiffness pro...

Approximate numerical techniques, for the solution of the elastic wave scattering problem over semi-infinite domains are reviewed. The approximations involve the representation of the half-space by a boundary condition described in terms of 2D boundary element discretizations. The classical BEM matrices are initially re-written into the form of a dense dynamic stiffness matrix and later approxi...

In a traditional finite element method for the simulation of deformable objects, the stiffness matrix depends on the shape of the tetrahedral elements. Ill-shaped elements containing large or small dihedral angles lead to an arbitrary large condition number of the stiffness matrix, thus slowing down the simulation. In addition, high modal frequencies cannot be simulated stably if an explicit nu...

Recalculating the subspace basis of a deformable body is a mandatory procedure for subspace simulation, after the body gets modified by interactive applications. However, using linear modal analysis to calculate the basis from scratch is known to be computationally expensive. In the paper, we show that the subspace of a modified body can be efficiently obtained from the subspace of its original...

A coupled model based on finite element method (FEM) and scaled boundary finite element method (SBFEM) for transient dynamic response of large-scale SSI systems is presented. The wellestablished FEM is used for modeling the near-field bounded domains. A local high-order transmitting boundary, which is based on SBFEM and the improved continued fraction solution for the dynamic stiffness matrix, ...

We investigate the buckling of a slender rod embedded in a soft elastomeric matrix through a combination of experiments, numerics and theory. Depending on the control parameters, both planar wavy (2D) or non-planar coiled (3D) configurations are observed in the post-buckling regime. Our analytical and numerical results indicate that the rod buckles into 2D configurations when the compression fo...

A numerical method is presented for stability analysis of cable–bar structures. An optimization problem is formulated to find the minimum value of the incremental total potential energy that depends on the direction of the incremental displacements. The penalty method with slack variables is used for representing the discontinuity in member stiffness. The tangent stiffness matrix is shifted to ...

In this paper Rannacher-Turek non-conforming rotated bilinear finite elements are applied for the numerical solution of second order elliptic boundary value problems. The preconditioned conjugate gradient method is used for the iterative solution of the arising linear algebraic system. A locally optimized construction for an M-matrix approximation of the global stiffness matrix is the first ste...