This paper presents an efficient and novel geometric flow-driven method for mesh optimization of segmented tetrahedral meshes with non-manifold boundary surfaces. The presented method is composed of geometric optimization and topological transformation techniques, so that both location and topology of vertices are optimized. Non-manifold boundary can be divided into manifold surface patches hav...

We consider the problem of solving linear systems of equations that arise in the numerical solution of singularly perturbed ordinary and partial differential equations of reaction-diffusion type. Standard discretization techniques are not suitable for such problems and, so, specially tailored methods are required, usually involving adapted or fitted meshes that resolve important features such a...

We consider the problem of solving linear systems of equations that arise in the numerical solution of singularly perturbed ordinary and partial differential equations of reaction-diffusion type. Standard discretization techniques are not suitable for such problems and, so, specially tailored methods are required, usually involving adapted or fitted meshes that resolve important features such a...

This paper presents an extension of the all-quad meshing algorithm called LayTracks to generate high quality hex and hexdominant meshes of 3D assembly models. LayTracks3D uses the mapping between the Medial Axis (MA) and the boundary of the 3D domain to decompose complex 3D domains into simpler domains called Tracks. Tracks in 3D are similar to tunnels with no branches and are symmetric, non-in...

We present a new solution to the well-known problems of edge collapses in nonconvex tetrahedral meshes. Additionally, our method is able to handle meshes with topologically non-trivial boundaries and to control the modification of the topology of the mesh’s boundary.

In this paper, the difference between the Alternating Direction Method (ADM) and the Non-Splitting Method (NSM) is investigated, while both methods applied to the simulations for 2-D multimaterial radiation diffusion issues. Although the ADM have the same accuracy orders with the NSM on the uniform meshes, the accuracy of ADM will decrease on the distorted meshes or the boundary of domain. Nume...

Details are given of a boundary-fitted mesh generation method for use in modelling free surface flow and water quality. A numerical method has been developed for generating conformal meshes for curvilinear polygonal and multiply-connected regions. The method is based on the Cauchy-Riemann conditions for the analytic function and is able to map a curvilinear polygonal region directly onto a regu...

We establish a mortar boundary element scheme for hypersingular boundary integral equations representing elliptic boundary value problems in three dimensions. We prove almost quasi-optimal convergence of the scheme in broken Sobolev norms of order 1/2. Sub-domain decompositions can be geometrically non-conforming and meshes must be quasi-uniform only on sub-domains. Numerical results confirm th...

The immersed boundary method is a numerical approach for simulating elastic structures which interact with a fluid flow. In many physical systems thermal fluctuations become significant at small scales and play a fundamental role. In this paper stochastic numerical methods are developed which extend the immersed boundary approach to account for thermal fluctuations by including appropriate stoc...

This research note presents an extension of all-quad meshing algorithm called LayTracks to generate high quality hex and hex-dominant meshes of 3D assembly models. LayTracks3D uses the mapping between the Medial Axis (MA) and the boundary of the 3D domain to decompose complex 3D domains into simpler domains called Tracks. Tracks in 3D are tunnels with no branches and are symmetric, non-intersec...