The use of implicit formulae in the solution of stiff ODEs gives rise to systems of nonlinear equations which are usually solved iteratively by a modified Newton scheme. The linear algebra costs associated with such schemes may form a substantial part of the overall cost of the solution. The work of W. H. Enright and M. S. Kamel attempts to reduce the cost of the iteration by automatically tran...

Fluid–structure interaction problems arise in many application fields such as flows around elastic structures or blood flow problems in arteries. One method for solving such a problem is based on a reduction to an equation on the interface, involving the so-called Steklov–Poincaré operators. This interface equation is solved by a Newton iteration for which directional derivatives with respect t...

Full Newton nonlinear iteration is compared to use of a defect correction approach rst order Jacobian second order residual for solving the steady state compressible ow equations The Jacobian is constructed numerically and solved using a PCG type method with block ILU k preconditioning Numerical tests are carried out using the NACA airfoil at various free stream Mach numbers and Reynolds number...

We present a Monte Carlo synthetic-acceleration method for solving the time-dependent, nonlinear, equilibrium diffusion equation in three-dimensions. The new scheme uses the adjoint Monte Carlo method as a relaxation step that accelerates standard Jacobi iteration. Results show that this method is 40% faster than regular Jacobi iteration and is competitive with Jacobi-preconditioned Conjugate G...

We present a new method for real-time physics-based simulation supporting many different types of hyperelastic materials. Previous methods such as Position Based or Projective Dynamics are fast, but support only limited selection of materials; even classical materials such as the Neo-Hookean elasticity are not supported. Recently, Xu et al. [2015] introduced new “spline-based materials” which c...

In this paper, we study iterative methods on the coefficients of the rational univariate representation (RUR) of a given algebraic set, called global Newton iteration. We compare two natural approaches to define locally quadratically convergent iterations: the first one involves Newton iteration applied to the approximate roots individually and then interpolation to find the RUR of these approx...

Algebraic Riccati equations (discrete-time or continuous-time) play a fundamental role in many problems in control theory. They arise in linear-quadratic regulator problems, H ∞ or H 2-control, model reduction problems and many others. In this talk we propose numerical methods for large discrete-time algebraic Riccati equations (DARE). We present block projection methods that allow us to comput...

PAD&APPROXIMANTS FOR THE SOLUTION OF A SYTEM OF NONLINEAR EQUATIONS ANNIE Cm-T? and PAUL VAN DER CRUYSSEN University of Antwerp, Department of Mathematics, Universiteitsplein 1, B-2610 Wihijk, Belgium (Receioed January 1981; and in revised form May 1982) Communicated by J. F. Traub Abstract-Let F: R4 *R’ and let x* be a simple root of the system of nonlinear equations F(x) = 0. We will construc...

We exhibit an algorithm which computes an approximation of the positive solutions of a family of boundary value problems with Neumann boundary conditions. Such solutions arise as the stationary solutions of a family of semilinear parabolic equations with Neumann boundary conditions. The algorithm is based on a nite dimensional Newton iteration associated with a suitable discretized version of t...

In this paper, we investigate the convergence behaviour of a class of regularized Newton methods for the solution of nonlinear inverse problems. In order to keep the overall numerical effort as small as possible, we propose to solve the linearized equations by certain semiiterative regularization methods, in particular, iterations with optimal speed of convergence. Our convergence rate analysis...