Accuracy of the Immersed Boundary Method in Fixed-Point Arithmetic
نویسندگان
چکیده
The immersed boundary (IB) method is an algorithm for simulating elastic structures immersed in a fluid. The IB method can be used, for example, to simulate blood flow in the heart. Even running on supercomputers, software implementations require on the order of seven CPU-days to simulate one heart beat. The IB method has significant, inherent, fine-grain parallelism available. This parallelism makes it a good candidate for implementation in hardware, such as a field-programmable gate array (FPGA). While floating-point arithmetic is possible on FPGAs, fixedpoint arithmetic is more efficient and takes less space to implement. This paper presents a study of the accuracy of a fixed-point implementation of the IB method.
منابع مشابه
A Fast Immersed Boundary Fourier Pseudo-spectral Method for Simulation of the Incompressible Flows
Abstract The present paper is devoted to implementation of the immersed boundary technique into the Fourier pseudo-spectral solution of the vorticity-velocity formulation of the two-dimensional incompressible Navier-Stokes equations. The immersed boundary conditions are implemented via direct modification of the convection and diffusion terms, and therefore, in contrast to some other similar ...
متن کاملDynamical Control of Computations Using the Family of Optimal Two-point Methods to Solve Nonlinear Equations
One of the considerable discussions for solving the nonlinear equations is to find the optimal iteration, and to use a proper termination criterion which is able to obtain a high accuracy for the numerical solution. In this paper, for a certain class of the family of optimal two-point methods, we propose a new scheme based on the stochastic arithmetic to find the optimal number of iterations in...
متن کاملIterative scheme based on boundary point method for common fixed point of strongly nonexpansive sequences
Let $C$ be a nonempty closed convex subset of a real Hilbert space $H$. Let ${S_n}$ and ${T_n}$ be sequences of nonexpansive self-mappings of $C$, where one of them is a strongly nonexpansive sequence. K. Aoyama and Y. Kimura introduced the iteration process $x_{n+1}=beta_nx_n+(1-beta_n)S_n(alpha_nu+(1-alpha_n)T_nx_n)$ for finding the common fixed point of ${S_n}$ and ${T_n}$, where $uin C$ is ...
متن کاملAIOSC: Analytical Integer Word-length Optimization based on System Characteristics for Recursive Fixed-point LTI Systems
The integer word-length optimization known as range analysis (RA) of the fixed-point designs is a challenging problem in high level synthesis and optimization of linear-time-invariant (LTI) systems. The analysis has significant effects on the resource usage, accuracy and efficiency of the final implementation, as well as the optimization time. Conventional methods in recursive LTI systems suffe...
متن کاملModified Fixed Grid Finite Element Method in the Analysis of 2D Linear Elastic Problems
In this paper, a modification on the fixed grid finite element method is presented and used in the solution of 2D linear elastic problems. This method uses non-boundary-fitted meshes for the numerical solution of partial differential equations. Special techniques are required to apply boundary conditions on the intersection of domain boundaries and non-boundary-fitted elements. Hence, a new met...
متن کامل