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We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…
Immersed boundary methods simplify mesh generation by embedding the domain of interest into an extended domain that is easy to mesh, introducing the challenge of dealing with cells that intersect the domain boundary. Combined with explicit…
A three dimensional parallel implementation of Multiscale Mixed Methods based on non-overlapping domain decomposition techniques is proposed for multi-core computers and its computational performance is assessed by means of numerical…
We apply a novel optimization scheme from the image processing and machine learning areas, a fast Primal-Dual method, to achieve controllable and realistic fluid simulations. While our method is generally applicable to many problems in…
In this paper, we present a novel approach to the problem of merging of B\'ezier curves with respect to the $L_2$-norm. We give illustrative examples to show that the solution of the conventional merging problem may not be suitable for…
An explicit moving boundary method for the numerical solution of time-dependent hyperbolic conservation laws on grids produced by the intersection of complex geometries with a regular Cartesian grid is presented. As it employs directional…
In this work we consider how surface-adherent bacterial biofilm communities respond in flowing systems. We simulate the fluid-structure interaction and separation process using the immersed boundary method. In these simulations we model and…
In this paper, we analyze the embedding cell method, an algorithm which has been developed for the numerical homogenization of metal-ceramic composite materials. We show the convergence of the iteration scheme of this algorithm and the…
The Immersed Boundary Method (IBM) is one of the popular one-fluid mixed Eulerian-Lagrangian methods to simulate motion of droplets. While the treatment of a moving complex boundary is an extremely time consuming and formidable task in a…
This paper serves to treat boundary conditions numerically with high order accuracy in order to match the two-stage fourth-order finite volume schemes for hyperbolic problems developed in [{\em J. Li and Z. Du, A two-stage fourth order…
We develop numerical methods to simulate the fluid-mechanical erosion of many bodies in two-dimensional Stokes flow. The broad aim is to simulate the erosion of a porous medium (e.g. groundwater flow) with grain-scale resolution. Our fluid…
Particle-in-cell merging algorithms aim to resample dynamically the six-dimensional phase space occupied by particles without distorting substantially the physical description of the system. Whereas various approaches have been proposed in…
The goal of this paper is to present a new efficient image segmentation method based on evolutionary computation which is a model inspired from human behavior. Based on this model, a four layer process for image segmentation is proposed…
Simulating wave propagation on discrete grid in time domain requires the description of both the parameters of the media and the values of the wave field at two different time steps within the simulated domain. For most practical cases this…
In this paper we propose a novel algorithm to combine two or more cellular complexes, providing a minimal fragmentation of the cells of the resulting complex. We introduce here the idea of arrangement generated by a collection of cellular…
It is known that data rates in standard cellular networks are limited due to inter-cell interference. An effective solution of this problem is to use the multi-cell cooperation idea. In Cloud Radio Access Network, which is a candidate…
We present a Cartesian cut-cell finite-volume method for sharp-interface two-phase diffusion problems in static geometries. The formulation follows a two-fluid approach: independent diffusion equations are discretized in each phase on a…
Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…
This paper tests a dielectric model for variation of hydration free energy with geometry of complex solutes in water. It works out some basic aspects of the theory of boundary integral methods for these problems. One aspect of the…
This article addresses the research question if and how the finite cell method, an embedded domain finite element method of high order, may be used in the simulation of metal deposition to harvest its computational efficiency. This…