ICES Report 04-58 INTEGRATION OF hp-ADAPTIVITY AND A TWO GRID SOLVER . II . ELECTROMAGNETIC PROBLEMS

We present implementation details and analyze convergence of a two-grid solver forming the core of a fully automatic hp-adaptive strategy for electromagnetic problems [9, 26]. The solver delivers a solution for a fine grid obtained from an arbitrary coarse hp grid by a global hp-refinement. The classical V-cycle algorithm combines an overlapping Block-Jacobi smoother with optimal relaxation, and a direct solve on the coarse grid. A theoretical analysis of the two grid solver is illustrated with numerical experiments. Several electromagnetic applications show the efficiency of combining the fully automatic hp-adaptive strategy with the two grid solver. This paper is a continuation of [25]. Acknowledgment The work has been partially supported by Air Force under Contract F49620-01-1-0043 and NSF under Grant DMS-0410030. The computations reported in this work were done through the National Science Foundation’s National Partnership for Advanced Computational Infrastructure. Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 2005 2. REPORT TYPE 3. DATES COVERED 00-00-2005 to 00-00-2005 4. TITLE AND SUBTITLE Integration of hp-Adaptability and a Two Grid Solver. II. Electromagnetic Problems 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Air Force Office of Scientific Research,875 North Randolph Street Suite 325,Arlington,VA,22203-1768 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S) 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited 13. SUPPLEMENTARY NOTES The original document contains color images. 14. ABSTRACT We present implementation details and analyze convergence of a two-grid solver forming the core of a fully automatic hp-adaptive strategy for electromagnetic problems [9, 26]. The solver delivers a solution for a ̄ne grid obtained from an arbitrary coarse hp grid by a global hp-re ̄nement. The classical V-cycle algorithm combines an overlapping Block-Jacobi smoother with optimal relaxation, and a direct solve on the coarse grid. A theoretical analysis of the two grid solver is illustrated with numerical experiments. Several electromagnetic applications show the e±ciency of combining the fully automatic hp-adaptive strategy with the two grid solver. This paper is a continuation of [25]. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES 54 19a. NAME OF RESPONSIBLE PERSON a. REPORT unclassified b. ABSTRACT unclassified c. THIS PAGE unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18