Dajana CONTE | NUMERICAL CALCULUS II

cod. 0512300033

NUMERICAL CALCULUS II

	0512300033
	DIPARTIMENTO DI MATEMATICA
	EQF6
	MATHEMATICS
	2019/2020

CURRICULUM MATEMATICA AD INDIRIZZO APPLICATIVO Cohort 2017/2018

	YEAR OF COURSE 3
	YEAR OF DIDACTIC SYSTEM 2016
	PRIMO SEMESTRE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/08	6	48	LESSONS	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS

PROFESSORS

	BEATRICE PATERNOSTER T Curriculum
	DAJANA CONTE Curriculum

	Objectives
	KNOWLEDGE AND UNDERSTANDING: THE AIM OF THE COURSE IS THE KNOWLEDGE OF TECHNIQUES FOR THE PROJECT OF PARALLEL CALCULUS FOR NUMERICAL LINEAR ALGEBRA. MOREOVER AIM OF THE COURSE IS THE KNOWLEDGE AND CRITICAL ANALYSIS OF THE MAIN NUMERICAL METHODS FOR THE SOLUTION OF PROBLEMS MODELED BY ORDINARY DIFFERENTIAL EQUATIONS, TOGETHER WITH THE DEVELOPMENT OF THE CORRESPONDING MATHEMATICAL SOFTWARE. APPLYING KNOWLEDGE AND UNDERSTANDING: THE AIM OF THE COURSE IS TO MAKE THE STUDENT CAPABLE TO DEVELOP PARALLEL METHODS FOR LINEAR ALGEBRA; SOLVE PROBLEMS OF SCIENTIFIC COMPUTING MODELED BY ORDINARY DIFFERENTIAL EQUATIONS (ODES) BY DEVELOPING AND USING MATHEMATICAL SOFTWARE WRITTEN BY THE STUDENTS AND SUITABLE CALCULUS ENVIRONMENTS; ANALYZE CONVERGENCE AND LINEAR STABILITY OF NUMERICAL METHODS FOR ODES.

KNOWLEDGE AND UNDERSTANDING:
THE AIM OF THE COURSE IS THE KNOWLEDGE OF TECHNIQUES FOR THE PROJECT OF PARALLEL CALCULUS FOR NUMERICAL LINEAR ALGEBRA. MOREOVER AIM OF THE COURSE IS THE KNOWLEDGE AND CRITICAL ANALYSIS OF THE MAIN NUMERICAL METHODS FOR THE SOLUTION OF PROBLEMS MODELED BY ORDINARY DIFFERENTIAL EQUATIONS, TOGETHER WITH THE DEVELOPMENT OF THE CORRESPONDING MATHEMATICAL SOFTWARE.

APPLYING KNOWLEDGE AND UNDERSTANDING:
THE AIM OF THE COURSE IS TO MAKE THE STUDENT CAPABLE TO DEVELOP PARALLEL METHODS FOR LINEAR ALGEBRA; SOLVE PROBLEMS OF SCIENTIFIC COMPUTING MODELED BY ORDINARY DIFFERENTIAL EQUATIONS (ODES) BY DEVELOPING AND USING MATHEMATICAL SOFTWARE WRITTEN BY THE STUDENTS AND SUITABLE CALCULUS ENVIRONMENTS; ANALYZE CONVERGENCE AND LINEAR STABILITY OF NUMERICAL METHODS FOR ODES.

	Prerequisites
	THEORY OF ORDINARY DIFFERENTIAL EQUATIONS. BASICS ON PROGRAMMING LANGUAGES MATLAB AND C.

	Contents
	ELEMENTS OF PARALLEL CALCULUS: PARALLEL ARCHITECTURES, MODELS AND COMPLEXITY PARAMETERS, STANDARD MPI (MESSAGE PASSING INTERFACE), EVALUATION PARAMETERS, PARALLEL ALGORITHMS FOR MATRIX-VECTOR AND MATRIX-MATRIX PRODUCTS, PARALLELIZATION TECHNIQUES. SCIENTIFIC PARALLEL CALCULUS ON GPUS (GRAPHICS PROCESSING UNITS). STRUCTUR OF A PROGRAM IN CUDA, KERNEL ORGANIZATION. NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS: ANALYTICAL APPROXIMATION METHODS, LNEAR MULTISTEP METHODS, PREDICTOR CORRECTOR METHODS, RUNGE-KUTTA METHODS. CONSISTENCY, CONVERGENCE, ZERO-STABILITY. THEORY OF WEAK STABILITY. STIFF SYSTEMS. STRUCTURE OF A VARIABLE STEPSIZE ALGORITHM.

Contents

ELEMENTS OF PARALLEL CALCULUS: PARALLEL ARCHITECTURES, MODELS AND COMPLEXITY PARAMETERS, STANDARD MPI (MESSAGE PASSING INTERFACE), EVALUATION PARAMETERS, PARALLEL ALGORITHMS FOR MATRIX-VECTOR AND MATRIX-MATRIX PRODUCTS, PARALLELIZATION TECHNIQUES.
SCIENTIFIC PARALLEL CALCULUS ON GPUS (GRAPHICS PROCESSING UNITS). STRUCTUR OF A PROGRAM IN CUDA, KERNEL ORGANIZATION.
NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS: ANALYTICAL APPROXIMATION METHODS, LNEAR MULTISTEP METHODS, PREDICTOR CORRECTOR METHODS, RUNGE-KUTTA METHODS. CONSISTENCY, CONVERGENCE, ZERO-STABILITY. THEORY OF WEAK STABILITY. STIFF SYSTEMS. STRUCTURE OF A VARIABLE STEPSIZE ALGORITHM.

	Teaching Methods
	LECTURES,PRACTICES,LABORATORY, PROJECTS ON DEVELOPMENT OF MATHEMATICAL SOFTWARE

	Verification of learning
	THE FINAL EXAM CONSISTS IN THE DISCUSSION OF A PRACTICAL PART IN THE LABORATORY AND AN ORAL PART ON THE CONTENTS OF THE COURSE. THE PRACTICAL PARTY REGARDS THE USE OF THE PARALLEL SOFTWARE AND OF THE MATHEMATICAL SOFTWARE DEVELOPED DURING THE TEACHING, TO BE APPLIED TO CERTAIN TEST PROBLEMS BASED ON ORDINARY DIFFERENTIAL EQUATIONS, TO CHECK THE ABILITY TO APPLY THE ACQUIRED KNOWLEDGE. THE ORAL PART REGARDS THE THEORETICAL CONTENTS OF TEACHING, IN ORDER TO CHECK THE ABILITY TO ANALYZING AND PRESENTING WITH RIGOR THE PROPERTIES OF NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS PRESENTED DURING THE LESSONS.

Verification of learning

THE FINAL EXAM CONSISTS IN THE DISCUSSION OF A PRACTICAL PART IN THE LABORATORY AND AN ORAL PART ON THE CONTENTS OF THE COURSE. THE PRACTICAL PARTY REGARDS THE USE OF THE PARALLEL SOFTWARE AND OF THE MATHEMATICAL SOFTWARE DEVELOPED DURING THE TEACHING, TO BE APPLIED TO CERTAIN TEST PROBLEMS BASED ON ORDINARY DIFFERENTIAL EQUATIONS, TO CHECK THE ABILITY TO APPLY THE ACQUIRED KNOWLEDGE. THE ORAL PART REGARDS THE THEORETICAL CONTENTS OF TEACHING, IN ORDER TO CHECK THE ABILITY TO ANALYZING AND PRESENTING WITH RIGOR THE PROPERTIES OF NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS PRESENTED DURING THE LESSONS.

	Texts
	J.D.LAMBERT, NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL SYSTEMS, J. WILEY & SONS, 1991. A. MURLI, LEZIONI DI CALCOLO PARALLELO, LIGUORI, 2006. MPI: HTTP://WWW.NETLIB.ORG/UTK/PAPERS/INTRO-MPI/INTRO-MPI.HTML

	More Information
	BEAPAT@UNISA.IT, DAJCONTE@UNISA.IT PLATFORM MTOUCH {MATHEMATICS ORIENTED VIRTUAL CLASSROOM HYPERSPACE} SU HTTPS://WWW.ELEARNING.DIPMAT.UNISA.IT/

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Dajana CONTE | NUMERICAL CALCULUS II