FMPM Features - Revision history

Nairnj: /* XPIC(k) and FMPM(k) Commands */

2026-04-12T18:53:15Z

XPIC(k) and FMPM(k) Commands

← Older revision		Revision as of 18:53, 12 April 2026
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	PDamping (alphapVsT),<(fractionPIC)>,<(XPICOrder)>		PDamping (alphapVsT),<(fractionPIC)>,<(XPICOrder)>

	where <tt>(fractionPIC)</tt> used to blend FLIP and XPIC(k) and <tt>(XPICOrder)</tt> was order of XPIC(k) calculations. These commands are no longer available the blending option has been removed. If these commands are found in old input files, ~~those commands~~ should convert to scheduling a [[PeriodicXPIC Custom Task]]. The <tt>(XPICOrder)</tt> is recommended to change to using FMPM(k). The <tt>(fractionPIC)</tt> option can be replaced by periodically using FMPM(k) with FLIP on other time steps rather then blending them on every time steps (''i.e.'', change <tt>(fractionPIC)=0.25</tt> to using FMPM(k) every 4<sup>th</sup> time step). The results are similar the periodic methods is much more efficient.		where <tt>(fractionPIC)</tt> used to blend FLIP and XPIC(k) and <tt>(XPICOrder)</tt> was order of XPIC(k) calculations. These commands are no longer available the blending option has been removed. If these commands are found in old input files, they should convert to scheduling a [[PeriodicXPIC Custom Task]]. The <tt>(XPICOrder)</tt> is recommended to change to using FMPM(k). The <tt>(fractionPIC)</tt> option can be replaced by periodically using FMPM(k) with FLIP on other time steps rather then blending them on every time steps (''i.e.'', change <tt>(fractionPIC)=0.25</tt> to using FMPM(k) every 4<sup>th</sup> time step). The results are similar the periodic methods is much more efficient.

	== References ==		== References ==

Nairnj: /* XPIC(k) and FMPM(k) Commands */

2026-04-12T18:52:31Z

XPIC(k) and FMPM(k) Commands

← Older revision		Revision as of 18:52, 12 April 2026
Line 22:		Line 22:
	PDamping (alphapVsT),<(fractionPIC)>,<(XPICOrder)>		PDamping (alphapVsT),<(fractionPIC)>,<(XPICOrder)>

	where <tt>(fractionPIC)</tt> used to blend FLIP and XPIC(k) and <tt>(XPICOrder)</tt> was order of XPIC(k) calculations. These commands are no longer available the blending option has be removed. If these commands are found in old input files, those commands should convert to scheduling a [[PeriodicXPIC Custom Task]]. The <tt>(XPICOrder)</tt> is recommended to change to using FMPM(k). The <tt>(fractionPIC)</tt> option can be replaced by periodically using FMPM(k) with FLIP on other time steps rather then blending them on every time steps (''i.e.'', change <tt>(fractionPIC)=0.25</tt> to using FMPM(k) every 4<sup>th</sup> time step). The results are similar the periodic methods is much more efficient.		where <tt>(fractionPIC)</tt> used to blend FLIP and XPIC(k) and <tt>(XPICOrder)</tt> was order of XPIC(k) calculations. These commands are no longer available the blending option has been removed. If these commands are found in old input files, those commands should convert to scheduling a [[PeriodicXPIC Custom Task]]. The <tt>(XPICOrder)</tt> is recommended to change to using FMPM(k). The <tt>(fractionPIC)</tt> option can be replaced by periodically using FMPM(k) with FLIP on other time steps rather then blending them on every time steps (''i.e.'', change <tt>(fractionPIC)=0.25</tt> to using FMPM(k) every 4<sup>th</sup> time step). The results are similar the periodic methods is much more efficient.

	== References ==		== References ==

Nairnj: /* Performance */

2026-04-12T18:51:27Z

Performance

← Older revision		Revision as of 18:51, 12 April 2026
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	== Performance ==		== Performance ==

	A drawback of FMPM(k) is that each higher order requires an extra extrapolation. The extra calculations scale with k*N where N is the number of particles in the problem. FMPM(k) is therefore less efficient than PIC or FLIP. In many problems, <tt>k=2</tt> already provides much improvement over PIC and reduces undesirable energy dissipation with minimal extra calculations. Larger <tt>k</tt> is often better with <tt>k=4</tt> appearing to provide much benefit without too much extra cost and ~~high~~ <tt>k</tt> eventually provides diminishing benefits. If used, very high <tt>k</tt> can become unstable unless the [[MPM Methods and Simulation Timing#Theory: MPM Time Step\|Courant–Friedrichs–Lewy factor (C)]] is reduced to below about 0.25 <ref name="FMPMrev"/>.		A drawback of FMPM(k) is that each higher order requires an extra extrapolation. The extra calculations scale with k*N where N is the number of particles in the problem. FMPM(k) is therefore less efficient than PIC or FLIP. In many problems, <tt>k=2</tt> already provides much improvement over PIC and reduces undesirable energy dissipation with minimal extra calculations. Larger <tt>k</tt> is often better with <tt>k=4</tt> appearing to provide much benefit without too much extra cost and higher <tt>k</tt> eventually provides diminishing benefits. If used, very high <tt>k</tt> can become unstable unless the [[MPM Methods and Simulation Timing#Theory: MPM Time Step\|Courant–Friedrichs–Lewy factor (C)]] is reduced to below about 0.25 <ref name="FMPMrev"/>.

	== XPIC(k) and FMPM(k) Commands ==		== XPIC(k) and FMPM(k) Commands ==

Nairnj: /* Performance */

2026-04-12T18:50:54Z

Performance

← Older revision		Revision as of 18:50, 12 April 2026
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	== Performance ==		== Performance ==

	A drawback of FMPM(k) is that each higher order requires an extra extrapolation. The extra calculations scale with k*N where N is the number of particles in the problem. FMPM(k) therefore less efficient than PIC or FLIP. In many problems, <tt>k=2</tt> already provides much improvement over PIC and reduces undesirable energy dissipation with minimal extra calculations. Larger <tt>k</tt> is often better with <tt>k=4</tt> appearing to provide much benefit without too much extra cost and high <tt>k</tt> eventually provides diminishing benefits. If used, very high <tt>k</tt> can become unstable unless the [[MPM Methods and Simulation Timing#Theory: MPM Time Step\|Courant–Friedrichs–Lewy factor (C)]] is reduced to below about 0.25 <ref name="FMPMrev"/>.		A drawback of FMPM(k) is that each higher order requires an extra extrapolation. The extra calculations scale with k*N where N is the number of particles in the problem. FMPM(k) is therefore less efficient than PIC or FLIP. In many problems, <tt>k=2</tt> already provides much improvement over PIC and reduces undesirable energy dissipation with minimal extra calculations. Larger <tt>k</tt> is often better with <tt>k=4</tt> appearing to provide much benefit without too much extra cost and high <tt>k</tt> eventually provides diminishing benefits. If used, very high <tt>k</tt> can become unstable unless the [[MPM Methods and Simulation Timing#Theory: MPM Time Step\|Courant–Friedrichs–Lewy factor (C)]] is reduced to below about 0.25 <ref name="FMPMrev"/>.

	== XPIC(k) and FMPM(k) Commands ==		== XPIC(k) and FMPM(k) Commands ==

Nairnj: /* Introduction */

2026-04-12T18:50:15Z

Introduction

← Older revision		Revision as of 18:50, 12 April 2026
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	The [[Damping Options#PIC Damping\|PIC method]] can be described as applying a projection operator that modifies (and filters) particle velocities before updating them with the grid acceleration. The problem with PIC is that its projection operator filters most problems too heavily resulting in significant dissipation of energy. The XPIC(k) methods was developed to reduce energy dissipation problem thereby filtering out noise that should enhances overall stability of MPM. XPIC(k) defines a series of new projection operators that can significantly reduce the over damping of PIC simulations. XPIC(k) is defined by an order <tt>k</tt>, where <tt>k=1</tt> is PIC, <tt>k>1</tt> is XPIC, and large <tt>k</tt> approaches a method with all null-space noise removed.		The [[Damping Options#PIC Damping\|PIC method]] can be described as applying a projection operator that modifies (and filters) particle velocities before updating them with the grid acceleration. The problem with PIC is that its projection operator filters most problems too heavily resulting in significant dissipation of energy. The XPIC(k) methods was developed to reduce energy dissipation problem thereby filtering out noise that should enhances overall stability of MPM. XPIC(k) defines a series of new projection operators that can significantly reduce the over damping of PIC simulations. XPIC(k) is defined by an order <tt>k</tt>, where <tt>k=1</tt> is PIC, <tt>k>1</tt> is XPIC, and large <tt>k</tt> approaches a method with all null-space noise removed.

	After deriving XPIC(k)<ref name="XPIC"/> methods, an incremental improvement was to show that XPIC style calculations are equivalent to implementing an MPM method that approximates the inverse of the full mass matrix. Use this revised interpretation, the XPIC(k) scheme was modifed to derive another method denoted FMPM(k)<ref name="FMPM"/>. FMPM(1) defines and improved form of PIC (compared to XPIC(1)) and higher orders also appear to further reduce dissipation compared to XPIC(k). Recent revisions for FMPM(k) have fixed issues related to boundary conditions and contact mechanics<ref name="FMPMrev"/>. Although both XPIC(k) and FMPM(k) are supported, ~~simulations~~ results show that FMPM(k) is better. XPIC(k) should only be used for comparison purposes.		After deriving XPIC(k)<ref name="XPIC"/> methods, an incremental improvement was to show that XPIC style calculations are equivalent to implementing an MPM method that approximates the inverse of the full mass matrix. Use this revised interpretation, the XPIC(k) scheme was modifed to derive another method denoted FMPM(k)<ref name="FMPM"/>. FMPM(1) defines and improved form of PIC (compared to XPIC(1)) and higher orders also appear to further reduce dissipation compared to XPIC(k). Recent revisions for FMPM(k) have fixed issues related to boundary conditions and contact mechanics<ref name="FMPMrev"/>. Although both XPIC(k) and FMPM(k) are both supported, simulation results show that FMPM(k) is better. XPIC(k) should only be used for comparison purposes.

	== Performance ==		== Performance ==

Nairnj: /* Introduction */

2026-04-12T18:49:26Z

Introduction

← Older revision		Revision as of 18:49, 12 April 2026
Line 5:		Line 5:
	The [[Damping Options#PIC Damping\|PIC method]] can be described as applying a projection operator that modifies (and filters) particle velocities before updating them with the grid acceleration. The problem with PIC is that its projection operator filters most problems too heavily resulting in significant dissipation of energy. The XPIC(k) methods was developed to reduce energy dissipation problem thereby filtering out noise that should enhances overall stability of MPM. XPIC(k) defines a series of new projection operators that can significantly reduce the over damping of PIC simulations. XPIC(k) is defined by an order <tt>k</tt>, where <tt>k=1</tt> is PIC, <tt>k>1</tt> is XPIC, and large <tt>k</tt> approaches a method with all null-space noise removed.		The [[Damping Options#PIC Damping\|PIC method]] can be described as applying a projection operator that modifies (and filters) particle velocities before updating them with the grid acceleration. The problem with PIC is that its projection operator filters most problems too heavily resulting in significant dissipation of energy. The XPIC(k) methods was developed to reduce energy dissipation problem thereby filtering out noise that should enhances overall stability of MPM. XPIC(k) defines a series of new projection operators that can significantly reduce the over damping of PIC simulations. XPIC(k) is defined by an order <tt>k</tt>, where <tt>k=1</tt> is PIC, <tt>k>1</tt> is XPIC, and large <tt>k</tt> approaches a method with all null-space noise removed.

	After deriving XPIC(k)<ref name="XPIC"/> methods, ~~another~~ improvement was to show that XPIC style calculations are equivalent to implementing an MPM method that approximates the inverse of the full mass matrix. Use this revised interpretation, the XPIC(k) scheme was modifed to derive another method denoted FMPM(k)<ref name="FMPM"/>. FMPM(1) defines and improved form of PIC (compared to XPIC(1)) and higher orders also appear to further reduce dissipation compared to XPIC(k). Recent revisions for FMPM(k) have fixed issues related to boundary conditions and contact mechanics<ref name="FMPMrev"/>. Although both XPIC(k) and FMPM(k) are supported, simulations results show that FMPM(k) is better. XPIC(k) should only be used for comparison purposes.		After deriving XPIC(k)<ref name="XPIC"/> methods, an incremental improvement was to show that XPIC style calculations are equivalent to implementing an MPM method that approximates the inverse of the full mass matrix. Use this revised interpretation, the XPIC(k) scheme was modifed to derive another method denoted FMPM(k)<ref name="FMPM"/>. FMPM(1) defines and improved form of PIC (compared to XPIC(1)) and higher orders also appear to further reduce dissipation compared to XPIC(k). Recent revisions for FMPM(k) have fixed issues related to boundary conditions and contact mechanics<ref name="FMPMrev"/>. Although both XPIC(k) and FMPM(k) are supported, simulations results show that FMPM(k) is better. XPIC(k) should only be used for comparison purposes.

	== Performance ==		== Performance ==

Nairnj at 18:48, 12 April 2026

2026-04-12T18:48:08Z

← Older revision		Revision as of 18:48, 12 April 2026
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	FMPM refers to variant of MPM that uses an approximation to the full mass matrix inverse rather then rely on lump mass matrix methods <ref name="FMPM"/><ref name="FMPMrev"/>. It is referred to as FMPM(k) where ``k'' is the order of approximation used to find the full mass matrix inverse. FMPM(k) is an incremental improvement an an early methods known as XPIC(k)<ref name="XPIC"/>. They are very similar, but FMPM(k) is now the preferred option.		FMPM refers to variant of MPM that uses an approximation to the full mass matrix inverse rather then rely on lump mass matrix methods <ref name="FMPM"/><ref name="FMPMrev"/>. It is referred to as FMPM(k) where ''k'' is the order of approximation used to find the full mass matrix inverse. FMPM(k) is an incremental improvement an an early methods known as XPIC(k)<ref name="XPIC"/>. They are very similar, but FMPM(k) is now the preferred option.

	== Introduction ==		== Introduction ==

Nairnj at 18:47, 12 April 2026

2026-04-12T18:47:55Z

← Older revision		Revision as of 18:47, 12 April 2026
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	FMPM~~(k)~~<ref name="FMPM"/> ~~and~~ XPIC(k)<ref name="XPIC"/> are ~~two improved forms of MPM. The page explains how to use XPIC(k) and~~ FMPM(k) ~~features~~.		FMPM refers to variant of MPM that uses an approximation to the full mass matrix inverse rather then rely on lump mass matrix methods <ref name="FMPM"/><ref name="FMPMrev"/>. It is referred to as FMPM(k) where ``k'' is the order of approximation used to find the full mass matrix inverse. FMPM(k) is an incremental improvement an an early methods known as XPIC(k)<ref name="XPIC"/>. They are very similar, but FMPM(k) is now the preferred option.

	== Introduction ==		== Introduction ==

Nairnj: Nairnj moved page XPIC Features to FMPM Features: To emphasize FMPM is better than XPIC

2026-04-12T18:44:04Z

Nairnj moved page XPIC Features to FMPM Features: To emphasize FMPM is better than XPIC

← Older revision	Revision as of 18:44, 12 April 2026
(No difference)

Nairnj at 18:31, 12 April 2026

2026-04-12T18:31:03Z

← Older revision		Revision as of 18:31, 12 April 2026
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	~~XPIC~~(k)<ref name="~~XPIC~~"/> and ~~FMPM~~(k)<ref name="~~FMPM~~"/> are two improved forms of MPM. The page explains how to use XPIC(k) and FMPM(k) features.		FMPM(k)<ref name="FMPM"/> and XPIC(k)<ref name="XPIC"/> are two improved forms of MPM. The page explains how to use XPIC(k) and FMPM(k) features.

	== Introduction ==		== Introduction ==