Module also offered within study programmes:
General information:
Code:
UBPJO-154
Name:
CAD/CAE Systems
Profile of education:
Academic (A)
Lecture language:
English
Semester:
Fall
Responsible teacher:
Paszyński Maciej (paszynsk@agh.edu.pl)
Academic teachers:
Paszyński Maciej (paszynsk@agh.edu.pl)
Module summary

Description of learning outcomes for module
MLO code Student after module completion has the knowledge/ knows how to/is able to Connections with FLO Method of learning outcomes verification (form of completion)
Social competence
M_K001 Knows basic principles of modeling geometries with B-splines within CAD systems Completion of laboratory classes
Skills
M_U001 Is able to solve model engineering problem using finite difference method and CAE system Completion of laboratory classes
M_U002 Is able to solve model engineering problem using finite element method and CAE system
Knowledge
M_W001 Knows the principles of the finite difference method Completion of laboratory classes
M_W002 Knows the principles of the finite element method Completion of laboratory classes
M_W003 Knows basic design principles of Computer Aided Design systems Completion of laboratory classes
M_W004 Knows basic principles of Computer Aided Engineering systems Completion of laboratory classes
M_W005 Knows how to model geometry using B-splines within CAD systems Completion of laboratory classes
FLO matrix in relation to forms of classes
MLO code Student after module completion has the knowledge/ knows how to/is able to Form of classes
Lecture
Audit. classes
Lab. classes
Project classes
Conv. seminar
Seminar classes
Pract. classes
Zaj. terenowe
Zaj. warsztatowe
Others
E-learning
Social competence
M_K001 Knows basic principles of modeling geometries with B-splines within CAD systems - - - - - - - - - - -
Skills
M_U001 Is able to solve model engineering problem using finite difference method and CAE system + - + - - - - - - - -
M_U002 Is able to solve model engineering problem using finite element method and CAE system + - + - - - - - - - -
Knowledge
M_W001 Knows the principles of the finite difference method + - + - - - - - - - -
M_W002 Knows the principles of the finite element method + - + - - - - - - - -
M_W003 Knows basic design principles of Computer Aided Design systems + - + - - - - - - - -
M_W004 Knows basic principles of Computer Aided Engineering systems + - + - - - - - - - -
M_W005 Knows how to model geometry using B-splines within CAD systems + - + - - - - - - - -
Module content
Lectures:
  1. Introduction to Computer Aided Design and Computer Aided Engineering (2 hours)

    CAD/CAE market. Basic steps of the engineering process: Modeling of geometry in CAD system, modeling of objects by B-splines and NURBS, generation of material data for particular objects, meshing for CAE computations, discretization by using finite difference or finite element method, solution of the system of linear equations by direct or iterative solver algorithm, analysis of the accuracy of the simulation, mesh adaptation, postprocessing

  2. Basic methods of Computer Aided Engineering: Finite element method (2 hours)

    Introduction to finite element method. Exemplary finite element method for heat transfer problem. Derivation of the formulation in 2D. Discretization methods. Interfacing with the solver algorithm.

  3. Mesh adaptation algorithms (2 hours)

    Introduction to the mesh adaptation algorithm. Automatic algorithm for hp adaptation. Design principles for object-oriented adaptive CAD/CAE systems. Exponential convergence of the numerical error with respect to the mesh size for the hp adaptive algorithm.

  4. Direct solvers utilized in CAD/CAE systems (2 hours)

    Mesh based solvers utilized in CAD/CAE systems. Multi-frontal solver algorithm and its applications. Parallel version of the multi-frontal solver algorithm for shared-memory and distributed memory architectures. Computational costs of the multi-frontal solvers.

  5. Summary of the lecture (2 hours)

    Comparison of computational costs of adaptive finite element method and isogeomtric finite element method, for sequential and parallel, distributed and shared memory simulations.

  6. Introduction to Computer Aided Design: modeling of geometry with B-splines and NURBS (2 hours)

    Basic principles of modeling of geometry with B-splines and NURBS. Know vectors, B-splines basis functions. Idea of Non-Uniform Rational B-splines (NURBS). Examples of modeling two and three dimensional objects.

  7. Introduction to Isogeometric analysis (2 hours)

    Utilization of the same basis functions for modeling of geometry and for engineering simulations. Integration of the engineering simulations in CAE systems. Computational costs of isogeometric analysis.

  8. Basic methods of Computer Aided Engineering: Finite difference method (2 hours)

    Introduction to finite difference method. Exemplary finite difference method for heat transfer problem. Derivation of the formulation in 1D, 2D and 3D. Discretization methods.
    Interfacing with the solver algorithm.

Laboratory classes:
  1. Installation of the virtual machine with MUMPS solver, compilations and linking of libraries (2 hours)

    Students download, compile and link the CAE environment in virtual linux machine.

  2. Implementation and execution of one dimensional finite difference method (2 hours)

    Student write a simple C code in virtual machine with one dimensional finite element method. They compile and link to MUMPS solver.

  3. Implementation and execution of two dimensional finite difference method (2 hours)

    Student write a simple C code in virtual machine with two dimensional finite element method. They compile and link to MUMPS solver. This is an extension of the previous lab for more complicated case.

  4. One dimensional hp adaptive finite element method (2 hours)

    Students install and compile one dimensional hp adaptive finite element method code and learn how to solve a prescribed engineering problem using the 1D code.

  5. Modeling geometries for two dimensional finite element method (2 hours)

    Students learn how to prepare an input file with geometry description for two dimensional hp adaptive finite element method.

  6. Comparison of convergence of h adaptive and p adaptive method in 2D hp-FEM (2 hours)

    Students play with two dimensional hp adaptive system and compares convergence methods for simple engineering problems.

  7. Solving challenging problems with CAD/CAE systems (2 hours)

    Students will implement some aspects of the model and execute the hp adaptive finite element method code for solution of the Stokes flow problem.

  8. Computational costs and memory usage of the solvers (2 hours)

    Students will experiment with limitations of the method by increasing the problem size and measuring execution times and memory usage of the solver (2 hours)

Student workload (ECTS credits balance)
Student activity form Student workload
Summary student workload 100 h
Module ECTS credits 4 ECTS
Participation in lectures 30 h
Participation in lectures 30 h
Preparation for classes 30 h
Realization of independently performed tasks 10 h
Additional information
Method of calculating the final grade:

1. It is necessary to obtain positive average grade from the labs
2. Final grade depends on the average grade obtained from the labs:
if sr>4.75 then OK:=5.0 else
if sr>4.25 then OK:=4.5 else
if sr>3.75 then OK:=4.0 else
if sr>3.25 then OK:=3.5 else OK:=3

Prerequisites and additional requirements:

Basics of C/C++ programming
Basics of linear algebra
Basics of PDE

Recommended literature and teaching resources:

Cottrell, J. Austin; Thomas J.R. Hughes, Yuri Bazilevs (October 2009). Isogeometric Analysis: Toward Integration of CAD and FEA. John Wiley & Sons. ISBN 978-0-470-74873-2
Demkowicz L. Computing with hp-Adaptive Finite Elements. Vol. 1Chapmann & Hall / CRC Press 2007

Scientific publications of module course instructors related to the topic of the module:

1 Maciej Paszynski, Jason Kurtz, Leszek Demkowicz, Parallel Fully Automatic hp-
Adaptive 2D Finite Element Package. Computer Methods in Applied Mechanics and Engineering, 195 (2006) 711-741.
2 Maciej Paszynski, Leszek Demkowicz, Parallel Fully Automatic hp-Adaptive 3D Finite Element Package. Engineering with Computers, 22 (2006) 255-276.
3 Pawel Matuszyk, Maciej Paszynski, Fully automatic hp adaptive finite element method for the Stokes problem in two dimensions. Computer Methods in Applied Mechanics and Engineering, 197 (2008) 4549-4558.
4 Nathan Collier, David Pardo, Lisandro Dalcin, Maciej Paszynski, Victor Calo, The cost of continuity: A study of the performance of isogeometric finite elements using direct solvers. Computer Methods in Applied Mechanics and Engineering, 213-216 (2012) 353-361.
5 Maciej Paszynski, Victor Calo, David Pardo, A direct solver with reutilization of previously-computed LU factorizations for h-adaptive finite element grids with point singularities. Computers and Mathematics with
Applications, 65, 8 (2013) 1140-1151.

Additional information:

Demkowicz L. Kurtz J., Pardo D., Paszyński M., Rachowicz W., Zdunek A., Computing with hp-Adaptive Finite Elements. Vol. 2: Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications, Chapmann & Hall / CRC Press 2007