Efficient solution of parabolic equations by polynomial approximation methods:
Abstract: "In this paper we take a new look at numerical techniques for solving parabolic equations by the method of lines. The main motivation for the proposed approach is the possibility to exploit a high degree of parallelism in a simple manner. The basic idea of the method is to approximate...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Urbana, Ill.
1990
|
| Series: | Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report
969 |
| Subjects: | |
| Summary: | Abstract: "In this paper we take a new look at numerical techniques for solving parabolic equations by the method of lines. The main motivation for the proposed approach is the possibility to exploit a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of very small dimension to a known vector. This is in turn computed accurately by exploiting well-known rational approximations to the exponential Since the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix by vector products, and as a result the algorithm can easily by parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present numerical experiments with the method on a Cray Y-MP and compare its performance with a few explicit and implicit algorithms. |
| Physical Description: | 32 Bl. graph. Darst. |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV008949946 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | t | ||
| 008 | 940206s1990 d||| |||| 00||| eng d | ||
| 035 | |a (OCoLC)22454249 | ||
| 035 | |a (DE-599)BVBBV008949946 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-29T | ||
| 100 | 1 | |a Gallopoulos, Efstratios |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Efficient solution of parabolic equations by polynomial approximation methods |c E. Gallopoulos ; Y. Saad |
| 264 | 1 | |a Urbana, Ill. |c 1990 | |
| 300 | |a 32 Bl. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report |v 969 | |
| 520 | 3 | |a Abstract: "In this paper we take a new look at numerical techniques for solving parabolic equations by the method of lines. The main motivation for the proposed approach is the possibility to exploit a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of very small dimension to a known vector. This is in turn computed accurately by exploiting well-known rational approximations to the exponential | |
| 520 | 3 | |a Since the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix by vector products, and as a result the algorithm can easily by parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present numerical experiments with the method on a Cray Y-MP and compare its performance with a few explicit and implicit algorithms. | |
| 650 | 4 | |a Approximation theory | |
| 650 | 4 | |a Parallel processing (Electronic computers) | |
| 700 | 1 | |a Saad, Yousef |e Verfasser |0 (DE-588)1025729978 |4 aut | |
| 830 | 0 | |a Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report |v 969 |w (DE-604)BV008930033 |9 969 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-005905557 | ||
Record in the Search Index
| _version_ | 1804123283163971584 |
|---|---|
| any_adam_object | |
| author | Gallopoulos, Efstratios Saad, Yousef |
| author_GND | (DE-588)1025729978 |
| author_facet | Gallopoulos, Efstratios Saad, Yousef |
| author_role | aut aut |
| author_sort | Gallopoulos, Efstratios |
| author_variant | e g eg y s ys |
| building | Verbundindex |
| bvnumber | BV008949946 |
| ctrlnum | (OCoLC)22454249 (DE-599)BVBBV008949946 |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02198nam a2200325 cb4500</leader><controlfield tag="001">BV008949946</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">940206s1990 d||| |||| 00||| eng d</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)22454249</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV008949946</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-29T</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Gallopoulos, Efstratios</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Efficient solution of parabolic equations by polynomial approximation methods</subfield><subfield code="c">E. Gallopoulos ; Y. Saad</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Urbana, Ill.</subfield><subfield code="c">1990</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">32 Bl.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report</subfield><subfield code="v">969</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="a">Abstract: "In this paper we take a new look at numerical techniques for solving parabolic equations by the method of lines. The main motivation for the proposed approach is the possibility to exploit a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of very small dimension to a known vector. This is in turn computed accurately by exploiting well-known rational approximations to the exponential</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="a">Since the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix by vector products, and as a result the algorithm can easily by parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present numerical experiments with the method on a Cray Y-MP and compare its performance with a few explicit and implicit algorithms.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Approximation theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Parallel processing (Electronic computers)</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Saad, Yousef</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1025729978</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report</subfield><subfield code="v">969</subfield><subfield code="w">(DE-604)BV008930033</subfield><subfield code="9">969</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-005905557</subfield></datafield></record></collection> |
| id | DE-604.BV008949946 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:27:18Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005905557 |
| oclc_num | 22454249 |
| open_access_boolean | |
| owner | DE-29T |
| owner_facet | DE-29T |
| physical | 32 Bl. graph. Darst. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| record_format | marc |
| series | Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report |
| series2 | Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report |
| spelling | Gallopoulos, Efstratios Verfasser aut Efficient solution of parabolic equations by polynomial approximation methods E. Gallopoulos ; Y. Saad Urbana, Ill. 1990 32 Bl. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report 969 Abstract: "In this paper we take a new look at numerical techniques for solving parabolic equations by the method of lines. The main motivation for the proposed approach is the possibility to exploit a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of very small dimension to a known vector. This is in turn computed accurately by exploiting well-known rational approximations to the exponential Since the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix by vector products, and as a result the algorithm can easily by parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present numerical experiments with the method on a Cray Y-MP and compare its performance with a few explicit and implicit algorithms. Approximation theory Parallel processing (Electronic computers) Saad, Yousef Verfasser (DE-588)1025729978 aut Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report 969 (DE-604)BV008930033 969 |
| spellingShingle | Gallopoulos, Efstratios Saad, Yousef Efficient solution of parabolic equations by polynomial approximation methods Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report Approximation theory Parallel processing (Electronic computers) |
| title | Efficient solution of parabolic equations by polynomial approximation methods |
| title_auth | Efficient solution of parabolic equations by polynomial approximation methods |
| title_exact_search | Efficient solution of parabolic equations by polynomial approximation methods |
| title_full | Efficient solution of parabolic equations by polynomial approximation methods E. Gallopoulos ; Y. Saad |
| title_fullStr | Efficient solution of parabolic equations by polynomial approximation methods E. Gallopoulos ; Y. Saad |
| title_full_unstemmed | Efficient solution of parabolic equations by polynomial approximation methods E. Gallopoulos ; Y. Saad |
| title_short | Efficient solution of parabolic equations by polynomial approximation methods |
| title_sort | efficient solution of parabolic equations by polynomial approximation methods |
| topic | Approximation theory Parallel processing (Electronic computers) |
| topic_facet | Approximation theory Parallel processing (Electronic computers) |
| volume_link | (DE-604)BV008930033 |
| work_keys_str_mv | AT gallopoulosefstratios efficientsolutionofparabolicequationsbypolynomialapproximationmethods AT saadyousef efficientsolutionofparabolicequationsbypolynomialapproximationmethods |