parallel adaptive simplical re meshing for deforming domain cfd computations deforming domains occur in many fields of computational fluid dynamics cfd such as interface tracking simulation of pumps and engines and fluid structure interaction the deformation of the domain presents a challenge to the integrity of the computational mesh substantial motion of the domain boundaries requires vertex motion and changes in mesh connectivity for cases of simple boundary motion or structured meshes predetermined changes to the mesh structure can be sufficient however without a priori knowledge of how the domain will change a more robust solution is required the present work offers a parallelized solution for simplical meshes that is well suited to extremely complex geometry the mesh continuously evolves without user intervention or the use of target meshes varying length scales imposed by evolving boundary curvatures and narrow gaps are resolved with a fast length scale algorithm the set of algorithms are incorporated into an object oriented code structure that permits broad application to a range of cfd problems the robustness and versatility of the algorithm is demonstrated in several examples representing motion of internal and external boundaries where the boundary motion may or may not be known a priori

generalized simulated annealing we discuss and illustrate a new stochastic algorithm generalized simulated annealing for computationally finding the global minimum of a given not necessarily convex energy cost function defined in a continuous d dimensional space this algorithm recovers as particular cases the so called classical boltzmann machine and fast cauchy machine simulated annealings and turns out to be quicker than both

velocity induced numerical solutions of reaction diffusion systems on continuously growing domains reaction diffusion systems have been widely studied in developmental biology chemistry and more recently in financial mathematics most of these systems comprise nonlinear reaction terms which makes it difficult to find closed form solutions it therefore becomes convenient to look for numerical solutions finite difference finite element finite volume and spectral methods are typical examples of the numerical methods used most of these methods are locally based schemes we examine the implications of mesh structure on numerically computed solutions of a well studied reaction diffusion model system on two dimensional fixed and growing domains the incorporation of domain growth creates an additional parameter the grid point velocity and this greatly influences the selection of certain symmetric solutions for the adi finite difference scheme when a uniform square mesh structure is used domain growth coupled with grid point velocity on a uniform square mesh stabilises certain patterns which are however very sensitive to any kind of perturbation in mesh structure we compare our results to those obtained by use of finite elements on unstructured triangular elements

solving the patient zero inverse problem by using generalized simulated annealing abstract identifying patient zero the initially infected source of a given outbreak is an important step in epidemiological investigations of both existing and emerging infectious diseases here the use of the generalized simulated annealing algorithm gsa to solve the inverse problem of finding the source of an outbreak is studied the classical disease natural histories susceptible infected si susceptible infected susceptible sis susceptible infected recovered sir and susceptible infected recovered susceptible sirs in a regular lattice are addressed both the position of patient zero and its time of infection are considered unknown the algorithm performance with respect to the generalization parameter q v and the fraction of infected nodes for whom infection was ascertained is assessed numerical experiments show the algorithm is able to retrieve the epidemic source with good accuracy even when is small but present no evidence to support that gsa performs better than its classical version our results suggest that simulated annealing could be a helpful tool for identifying patient zero in an outbreak where not all cases can be ascertained

multiple positive and 2 nodal symmetric solutions of elliptic problems with critical nonlinearity abstract we consider the problem u a x u f x u 2 2 u in u 0 on where is a bounded smooth domain in r n n 4 2 2 n n 2 is the critical sobolev exponent and a f are continuous functions we assume that a and f are invariant under the action of a group of orthogonal transformations we obtain multiplicity results which contain information about the symmetry and symmetry breaking properties of the solutions and about their nodal domains our results include new multiplicity results for the brezis nirenberg problem u u u 2 2 u in u 0 on

discontinuous galerkin finite element methods for incompressible non linear elasticity abstract a discontinuous galerkin finite element method dgfem for incompressible non linear elasticity is derived one of the limitations of the continuous galerkin finite element method cgfem when applied to incompressible elasticity is that the accuracy of the numerical solution may be adversely affected by the phenomenon known as locking this may prevent the use of a low order polynomial approximation to the displacement on each element we demonstrate using simulations that the dgfem presented here does not suffer from this drawback two further advantages in this setting of this dgfem over cgfems are that i highly anisotropic meshes meshes containing elements with a very high aspect ratio may be used without significantly degrading the accuracy of the solution and ii discontinuities in the elasticity parameters are handled more effectively

gradient flows and variational principles for cardiac electrophysiology toward efficient and robust numerical simulations of the electrical activity of the heart the computer simulation of the electrical activity of the heart has experienced tremendous advances in the last decade however the acceptance of computational methods in the medical community will largely depend on their reliability efficiency and robustness in this work we present a gradient flow reformulation of the cardiac electrophysiology equations and propose a minimax variational principle for the time discretized electrophysiology problem based on results from variational analysis we derive bounds on the time step size that guarantee the existence and uniqueness of the saddle point and in turn of the weak solution of the electrophysiology incremental problem we also show conditions under which the minimax problem is equivalent to an effective minimization principle which is amenable to a rayleigh ritz finite element analysis the derived time step bounds guarantee the strict convexity of the objective function resulting from spatial discretization thus ensuring the convergence of gradient descent methods the proposed theory is applied to the widely employed fitzhugh nagumo model which is shown to conform to the variational framework proposed in this work the applicability of the method and its implications on the robustness of time integration are demonstrated by way of numerical simulations of the electrical behavior in a single cell and 3d wedge and biventricular geometries we envision that the proposed framework will open the door to the development of robust and efficient electrophysiology models and simulations

inf sup conditions for twofold saddle point problems necessary and sufficient conditions for existence and uniqueness of solutions are developed for twofold saddle point problems which arise in mixed formulations of problems in continuum mechanics this work extends the classical saddle point theory to accommodate nonlinear constitutive relations and the twofold saddle structure application to problems in incompressible fluid mechanics employing symmetric tensor finite elements for the stress approximation is presented

best constant in critical sobolev inequalities of second order in the presence of symmetries abstract let m g be a smooth compact riemannian manifold we first give the value of the best first constant for the critical embedding h 2 m l 2 m for second order sobolev spaces of functions invariant by some subgroup of the isometry group of m g we also prove that we can take 0 in the corresponding inequality under some geometric assumptions as an application we give a sufficient condition for the existence of a smooth positive symmetric solution to a critical equation with a symmetric paneitz branson type operator a sufficient condition for the existence of a nodal solution to such an equation is also derived we eventually prove a multiplicity result for such an equation

primal mixed formulations for reaction diffusion systems on deforming domains we propose a finite element formulation for a coupled elasticity reaction diffusion system written in a fully lagrangian form and governing the spatio temporal interaction of species inside an elastic or hyper elastic body a primal weak formulation is the baseline model for the reaction diffusion system written in the deformed domain and a finite element method with piecewise linear approximations is employed for its spatial discretization on the other hand the strain is introduced as mixed variable in the equations of elastodynamics which in turn acts as coupling field needed to update the diffusion tensor of the modified reaction diffusion system written in a deformed domain the discrete mechanical problem yields a mixed finite element scheme based on row wise raviart thomas elements for stresses brezzi douglas marini elements for displacements and piecewise constant pressure approximations the application of the present framework in the study of several coupled biological systems on deforming geometries in two and three spatial dimensions is discussed and some illustrative examples are provided and extensively analyzed

multiplicity of solutions for elliptic quasilinear equations with critical exponent on compact manifolds abstract this paper deals with some perturbation of the so called generalized prescribed scalar curvature type equations on compact riemannian manifolds these equations are nonlinear of critical sobolev growth and involve the p laplacian sufficient conditions are given to have multiple positive solutions

generalized metropolis dynamics with a generalized master equation an approach for time independent and time dependent monte carlo simulations of generalized spin systems the extension of boltzmann gibbs thermostatistics proposed by tsallis introduces an additional parameter q to the inverse temperature here we show that a previously introduced generalized metropolis dynamics to evolve spin models is not local and does not obey the detailed energy balance in this dynamics locality is only retrieved for q 1 which corresponds to the standard metropolis algorithm nonlocality implies very time consuming computer calculations since the energy of the whole system must be reevaluated when a single spin is flipped to circumvent this costly calculation we propose a generalized master equation which gives rise to a local generalized metropolis dynamics that obeys the detailed energy balance to compare the different critical values obtained with other generalized dynamics we perform monte carlo simulations in equilibrium for the ising model by using short time nonequilibrium numerical simulations we also calculate for this model the critical temperature and the static and dynamical critical exponents as functions of q even for q 1 we show that suitable time evolving power laws can be found for each initial condition our numerical experiments corroborate the literature results when we use nonlocal dynamics showing that short time parameter determination works also in this case however the dynamics governed by the new master equation leads to different results for critical temperatures and also the critical exponents affecting universality classes we further propose a simple algorithm to optimize modeling the time evolution with a power law considering in a log log plot two successive refinements

entire nonradial solutions for non cooperative coupled elliptic system with critical exponents in r3 abstract we consider the following coupled elliptic system s n u 1 u n 2 n 2 u 2 n 2 v n n 2 in r n v 2 v n 2 n 2 v 2 n 2 u n n 2 in r n u v 0 u v d 1 2 r n where n 3 1 2 are two positive constants and 0 is the coupling constant when n 3 we prove the existence of infinitely many positive nonradial solutions

coupling remeshed particle and phase field methods for the simulation of reaction diffusion on the surface and the interior of deforming geometries reaction diffusion systems on the surface and the interior of complex domains are potent models of growth in living organisms the simulation of these models requires numerical methods capable of handling large deformations and the accurate coupling of the evolution of substances in the lumen and on the surface of the deforming geometries here we develop a novel computational method to handle such problems by combining a remeshed particle method with a phase field method remeshed particle methods are well suited to discretizing deforming geometries while the phase field method is used to impose boundary conditions that effectuate the coupling of substances evolving in their lumen and on their surfaces we demonstrate that this hybrid method enables for the first time the accurate coupling of reaction diffusion on a deformable surface and its interior the method is validated on benchmark problems and the effect of lumen diffusion to a pattern forming reaction diffusion system on a deforming surface is

krylov implicit integration factor methods for spatial discretization on high dimensional unstructured meshes application to discontinuous galerkin methods abstract integration factor methods are a class of exactly linear part time discretization methods in q nie y t zhang r zhao efficient semi implicit schemes for stiff systems journal of computational physics 214 2006 521 537 a class of efficient implicit integration factor iif methods were developed for solving systems with both stiff linear and nonlinear terms arising from spatial discretization of time dependent partial differential equations pdes with linear high order terms and stiff lower order nonlinear terms the tremendous challenge in applying iif temporal discretization for pdes on high spatial dimensions is how to evaluate the matrix exponential operator efficiently for spatial discretization on unstructured meshes to solve pdes on complex geometrical domains how to efficiently apply the iif temporal discretization was open in this paper we solve this problem by applying the krylov subspace approximations to the matrix exponential operator then we apply this novel time discretization technique to discontinuous galerkin dg methods on unstructured meshes for solving reaction diffusion equations numerical examples are shown to demonstrate the accuracy efficiency and robustness of the method in resolving the stiffness of the dg spatial operator for reaction diffusion pdes application of the method to a mathematical model in pattern formation during zebrafish embryo development shall be shown

multi travelling waves for the nonlinear klein gordon equation for the nonlinear klein gordon equation in r 1 d we prove the existence of multi solitary waves made of any number n of decoupled bound states this extends the work of cote and munoz forum math sigma 2 2014 which was restricted to ground states as were most previous similar results for other nonlinear dispersive and wave models

existence and multiplicity of nodal solutions for nonlinear elliptic equations with critical sobolev growth abstract let be a smooth bounded domain of r n n 3 and let a x and f x be two smooth functions defined on a neighbourhood of first we study the existence of nodal solutions for the equation u a x u f x u 4 n 2 u on u 0 on in particular when is a solid torus of r 3 we describe three infinity of pairs of solutions of the equation u u 4 n 2 u on u 0 on afterwards we study the equation when the zero dirichlet condition on the boundary is replaced by a non zero dirichlet condition

solutions nodales sur les varietes riemanniennes resume nodal solutions of nonlinear pde with critical growth are obtained on com pact manifolds the variational method and bifurcations theory are used to con struct a branch of nodal solutions consequences for other pde are suggested

multiple solutions of a critical polyharmonic equation we prove that for n 2m the equation mu u 4m n 2mu on rn has a sequence of nodal finite energy solutions which is unbounded in dm 2 rn this generalizes a classical result of weiyue ding for m 1

susceptible infected recovered model with recurrent infection abstract we analyze a stochastic lattice model describing the spreading of a disease among a community composed by susceptible infected and removed individuals a susceptible individual becomes infected catalytically an infected individual may spontaneously either become recovered that is acquire a permanent immunization or become again susceptible the critical properties including the phase diagram is obtained by means of mean field theories as well as numerical simulations the model is found to belong to the universality class of dynamic percolation except when the recovering rate vanishes in which case the model belongs to the directed percolation universality class

locking free finite element methods for linear and nonlinear elasticity in 2d and 3d abstract the uniform convergence of finite element approximations based on a modified hu washizu formulation for the nearly incompressible linear elasticity is analyzed we show the optimal and robust convergence of the displacement based discrete formulation in the nearly incompressible case with the choice of approximations based on quadrilateral and hexahedral elements these choices include bases that are well known as well as newly constructed bases starting from a suitable three field problem we extend our dependent three field formulation to geometrically nonlinear elasticity with saint venant kirchhoff law additionally an dependent three field formulation for a general hyperelastic material model is proposed a range of numerical examples using different material laws for small and large strain elasticity is presented

the second yamabe invariant let m g be a compact riemannian manifold of dimension n 3 we define the second yamabe invariant as the infimum of the second eigenvalue of the yamabe operator over the metrics conformal to g and of volume 1 we study when it is attained as an application we find nodal solutions of the yamabe equation