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Theory Manual
This manual provides detailed information about the theory used in the Altair Radioss Solver.
Large Displacement Finite Element Analysis Theory Manual
Radioss Parallelization
The performance criterion in the computation was always an essential point in the architectural conception of Radioss. At first, the program has been largely optimized for the vectored super-calculators like CRAY. Then, a first parallel version SMP made possible the exploration of shared memory on processors.
Measure of Performance

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Overview
Radioss^® is a leading explicit finite element solver for crash and impact simulation.
Tutorials
Discover Radioss functionality with interactive tutorials.
User Guide
This manual provides details on the features, functionality, and simulation methods available in Altair Radioss.
Reference Guide
This manual provides a detailed list of all the input keywords and options available in Radioss.
Example Guide
This manual presents examples solved using Radioss with regard to common problem types.
Verification Problems
This manual presents solved verification models.
Frequently Asked Questions
This section provides quick responses to typical and frequently asked questions regarding Radioss.
Theory Manual
This manual provides detailed information about the theory used in the Altair Radioss Solver.
- Large Displacement Finite Element Analysis Theory Manual
  - Introduction
    Nonlinear finite element analyses confront users with many choices. An understanding of the fundamental concepts of nonlinear finite element analysis is necessary if you do not want to use the finite element program as a black box. The purpose of this manual is to describe the numerical methods included in Radioss.
  - Basic Equations
  - Finite Element Formulation
  - Dynamic Analysis
  - Element Library
    Radioss element library contains elements for one, two or three dimensional problems.
  - Kinematic Constraints
    Kinematic constraints are boundary conditions that are placed on nodal velocities. They are mutually exclusive for each degree of freedom (DOF), and there can only be one constraint per DOF.
  - Linear Stability
    The stability of solution concerns the evolution of a process subjected to small perturbations. A process is considered to be stable if small perturbations of initial data result in small changes in the solution. The theory of stability can be applied to a variety of computational problems.
  - Interfaces
    Interfaces solve the contact and impact conditions between two parts of a model.
  - Material Laws
    A large variety of materials is used in the structural components and must be modeled in stress analysis problems. For any kind of these materials a range of constitutive laws is available to describe by a mathematical approach the behavior of the material.
  - Monitored Volume
    An airbag is defined as a monitored volume. A monitored volume is defined as having one or more 3 or 4 node shell property sets.
  - Static
    Explicit scheme is generally used for time integration in Radioss, in which velocities and displacements are obtained by direct integration of nodal accelerations.
  - Radioss Parallelization
    The performance criterion in the computation was always an essential point in the architectural conception of Radioss. At first, the program has been largely optimized for the vectored super-calculators like CRAY. Then, a first parallel version SMP made possible the exploration of shared memory on processors.
    - Measure of Performance
    - Shared Memory Processors (SMP)
    - Single Program Multiple Data (SPMD)
    - Hybrid Massively Parallel Program (HMPP)
      The Hybrid MPP combines the best of the SMP and SPMD parallel versions inside a unique code.
- ALE, CFD and SPH Theory Manual
- Appendix A: Basic Relations of Elasticity
User Subroutines
This manual describes the interface between Altair Radioss and user subroutines.

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Measure of Performance

The Speed-Up is the ratio of sequential time $T (1)$ and the parallel time on $P$ processors $T (P)$ :

S (P) = T (1) / T (P)

The efficiency is defined as:

E (P) = S (P) / P; E (P) \leq 1

The Amdahl’s law for multitasking is used to determine the speed-up:

S (P) = \frac{(T_{S e q} + T_{P a r})}{(T_{S e q} + \frac{T_{P a r}}{P})}

Where, $T_{P a r}$ and $T_{S e q}$ are the computation times respectively related to parallel and non-parallel parts. As $T_{S e q} + T_{P a r} = 1$ , write:

S (P) = \frac{1}{(T_{S e q} + \frac{T_{P a r}}{P})}

The limit value can be obtained when the process number tends to infinite:

S (\infty) = \frac{1}{T_{S e q}}

Table 1 provides the Speed-Up in function of number of processors and the rate of parallelization in the program. It can be seen that if the rate of parallelization is less 95%, the computation acceleration will not be greater than 20; however, the number of processors. This means that to obtain a good scalability of a code, at least 99% of the program must be parallel.

Table 1. Speed-up in Function of Process Number and Parallelization
Process Number Seq / P	2	4	8	16	32	64	128	$\infty$
100%	2.0	4.0	8.0	16.0	32.0	64.0	128.	$\infty$
99%	2.0	3.9	7.5	13.9	24.4	39.3	56.4	100.
98%	2.0	3.8	7.0	12.3	19.8	28.3	36.2	50.0
97%	1.9	3.7	6.6	11.0	16.5	22.1	26.6	33.3
96%	1.9	3.6	6.3	10.0	14.3	18.2	21.1	25.0
95%	1.9	3.5	5.9	9.1	12.5	15.4	17.4	20.0
90%	1.8	3.0	4.7	6.4	7.8	8.7	9.3	10.0
50%	1.3	1.6	1.8	1.9	1.9	2.0	2.0	2.0